STAAD-PRO-V8i

V8i

Release Release STAAD.Pro 20.07. 20.07.08.XX 08.XX Date last updated: 10 October 2011

STAAD.Pro V8i (SELECTseries 3) is a suite of proprietary proprietary computer computer programs of Rese Research arch Engineers, a Bentley Solutions Center. Although every effort has been made to ensure the correctness of these programs, neither REI nor Bentley Systems will accept responsibility for any mistake, error or misrepresentation in or as a result of the usage of these programs.

Verification Manual

iii

1 Plane Truss: Support Reactions Due to a Joint Load

1

2 Natural Frequency Calculation

5

3 Deflection and Moments for a Plate-Bending Finite Element

9

4 Support Reactions for a Simple Frame

15

5 Deflection and stress for a simple beam

21

6 Plane Frame with no Sidesway

27

7 Plane Truss Joint Deflection

33

8 Unequal Plane frame with Sidesway

39

9 Multiple level plane frame with horizontal loads

45

10 Forces in a Space Frame

51

11 Temperature load in different materials

57

12 Def lection and stress of a truss system

63

13 Steel Design per 1989 AISC Code

69

14 Concrete Design per ACI 318 Code

81

15 Natural Modes of a Simple Beam

87

16 Natural Frequencies of a Circular Plate

95

17 Natural Frequencies of a Rectangular Plate

103

18 Natural Modes of a Framework

111

19 Response of a Simply Supported Beam to a Shock Spectrum

121

20 Thermal Loading on a Simply Supported Rectangular Plate

129

21 Deflection Calculation Through Pushover Analysis

143

22 Fixed – Fixed Beam Excited by Harmonic Distributed Load

153

iv — STAAD.Pro

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To view the End User License Agreement for this product, review: eula_en.pdf .

Verification Manual

v

To find the support reactions due to a joint load in a plane truss.

Timoshenko, S., “Strength of Materials,” Part 1, D. Van Nostrand Co., Inc., 3 rd edition, 1956, page 346, problem 3.

Determine the horizontal reaction at support 4 of the system. Figure 1-1: Plane truss

Table 1-1: Comparison of Support Reaction, in kips, for verification problem no. 1 Result Type

R

4

Theory

8.77

STAAD Basic Solver

8.77

STAAD Advanced Solver

8.77

Verification Manual

1


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:26 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PLANE TRUSS INPUT FILE: ver01.STD 2. * FILE: VER01.STD 3. * 4. * REFERENCE `STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO 5. * PAGE 346 PROBLEM NO. 3. THE ANSWER IS REACTION = 0.877P. 6. * THEREFORE IF P=10, REACTION = 8.77 7. * 8. UNITS INCH KIP 9. JOINT COORD 10. 1 0. 0. ; 2 150. 100. ; 3 150. 50. ; 4 300. 0. 11. MEMBER INCI 12. 1 1 2 ; 2 1 3 ; 3 2 3 ; 4 2 4 ; 5 3 4 13. MEMB PROP 14. 1 4 PRIS AX 5.0 ; 2 5 PRIS AX 3.0 ; 3 PRIS AX 2 15. CONSTANT ; E 30000. ALL 16. SUPPORT ; 1 4 PINNED 17. LOADING 1 18. JOINT LOAD ; 2 FY -10. 19. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 5/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 2/ 2/ 4 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB :A PLANE TRUSS -- PAGE NO. 2 * FILE: VER01.STD 20. PRINT REACTION :A PLANE TRUSS -- PAGE NO. 3 * FILE: VER01.STD SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = TRUSS ----------------JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 8.77 5.00 0.00 0.00 0.00 0.00 4 1 -8.77 5.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 21. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:26 **** :A PLANE TRUSS -- PAGE NO. 4 * FILE: VER01.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 *

2 — STAAD.Pro


* GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A PLANE TRUSS -- PAGE NO. 5 * FILE: VER01.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb

Verification Manual

3


11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

4 — STAAD.Pro

To find the period of free vibration for a beam supported on two springs with a point mass.

Timoshenko, S., Young, D., and Weaver, W., “Vibration Problems in Engineering,” John Wiley & Sons, 4th edition, 1974. page 11, problem 1.1-3.

A simple beam is supported by two spring as shown in the figure. Neglectin g the distributed mass of the beam, calculate the period of free vibration of the beam subjected to a load of W. Figure 2-1: Beam supported on springs

EI = 30000.0 ksi A = 7.0 ft B = 3.0 ft. W = 1000 lbf K = 300.0 lb/in.

Table 2-1: Comparison of period, in sec., for verification problem no. 2 Result Type

Period, sec

Theory

0.533

STAAD Basic Solver

0.533


0.533

Verification Manual

5


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:31 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS INPUT FILE: ver02.STD 2. * FILE: VER02.STD 3. * 4. * REFERENCE: TIMOSHENKO,YOUNG,WEAVER, "VIBRATION PROBLEMS IN 5. * ENGINEERING", 4TH EDITION, JOHN WILEY & SONS, 6. * NEW YORK, 1974, PAGE 11, PROB 1.1-3 7. * THE ANSWER IN THE BOOK IS T = 0.533 SEC., VIZ., F = 1.876 CPS 8. * 9. UNIT POUND FEET 10. JOINT COORD ; 1 0. 0. ; 2 7. 0. ; 3 10. 0. 11. MEMB INCI ; 1 1 2 2 12. UNIT INCH 13. SUPPORT 14. 1 3 FIXED BUT MZ KFY 300. 15. MEMB PROP ; 1 2 PRIS AX 1. IZ 1. 16. CONSTANT ; E 30E6 ALL 17. CUT OFF MODE SHAPE 1 18. LOADING 1 1000 LB LOAD AT JOINT 2 19. JOINT LOAD ; 2 FY -1000. 20. MODAL CALCULATION 21. PERFORM ANALYS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 3/ 2/ 2 :NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 2 * FILE: VER02.STD SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 5 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 7 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB NUMBER OF MODES REQUESTED = 1 NUMBER OF EXISTING MASSES IN THE MODEL = 1 NUMBER OF MODES THAT WILL BE USED = 1 :NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 3 * FILE: VER02.STD CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 1.876 0.53317 2.047E-16 MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED MODE X Y Z WEIGHT 1 0.000000E+00 9.999999E+02 0.000000E+00 9.999999E+02 MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 0.00100.00 0.00 0.000 100.000 0.000 22. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:31 **** :NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 4 * FILE: VER02.STD ************************************************************

6 — STAAD.Pro


* For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 5 * FILE: VER02.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb

Verification Manual

7


11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

8 — STAAD.Pro

To find the deflection and moments for plate-bending finite element due to a pressure load.

Simple hand calculation by considering the entire structure as a cantilever beam.

A simple cantilever plate is divided into 12 4-noded finite elements. A uniform pressure load is applied and the maximum deflection at the tip of the cantilever and the maximum bending at the support are calculated. Figure 3-1: Finite element mesh of cantilevered plate.

Plate thickness = 25 mm Uniform pressure= 5 N/mm 2 Plate length = 6 spaces at 50 mm = 300 mm Plate width = 2 space at 50 mm = 100 mm

Verification Manual

9

3 Deflection and Moments for a Plate-Bending F inite Element

Max. deflection = WL3/8EI Where: WL3/8EI = [(5 · 300 · 100) · (300) 3] / [8 · (210 · 10 3N/mm2)x(100 · 253/12)] = (405 · 1010) / (21,875 · 107) = 18.51 mm Max. moment = WL/2 = (5 · 300 · 100) · 300/2 = 22.5(10) 6N·mm = 22.5 KN·m

Table 3-1: Comparison of max. defl. and max. moment for verification problem no. 3 Result Type

δ

max

M

(mm)

max

10 — STAAD.Pro

(KN·m)

Hand Calculation

STAAD Basic Solver


18.51

18.20

18.20

22.50

22.50

22.50

3 Deflection and Moments for a P late-Bending Finite Element

**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:35 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE FINITE ELEMENT VERIFICATION INPUT FILE: ver03.STD 2. * 3. * FILE : VER03.STD 4. * 5. * DEFLECTION OF A CANTILEVER PLATE UNDER UNIFORM PRESSURE. 6. * COMPARISON WITH ESTABLISHED FORMULA (WL^3/8EI) 7. * 8. UNIT KNS MMS 9. JOINT COORDINATES 10. 1 0 0 0 7 300 0 0 11. REPEAT 2 0 50 0 12. * 13. ELEMENT INCIDENCE 14. 1 1 2 9 8 TO 6 15. REPEAT 1 6 7 16. * 17. ELEMENT PROP 18. 1 TO 12 THICK 25.0 19. * 20. CONSTANT 21. E 210.0 ALL 22. POISSON STEEL ALL 23. * 24. SUPPORT 25. 1 8 15 FIXED 26. * 27. UNIT NEWTON 28. LOAD 1 5N/SQ.MM. UNIFORM LOAD 29. ELEMENT LOAD 30. 1 TO 12 PRESSURE 5.0 31. * 32. PERFORM ANALYSIS FINITE ELEMENT VERIFICATION -- PAGE NO. * P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 21/ 12/ 3 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 8/ 5/ 30 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 108 SIZE OF STIFFNESS MATRIX = 4 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.1/ 120711.0 MB 33. * 34. PRINT DISPLACEMENT LIST 14 FINITE ELEMENT VERIFICATION -- PAGE NO. * JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE -----------------JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 14 1 0.0000 0.0000 1.8159 0.0000 -0.0813 0.0000 ************** END OF LATEST ANALYSIS RESULT ************** 35. * 36. UNIT KN METER 37. PRINT REACTION

2

3

Verification Manual

11

3 Deflection and Moments for a Plate-Bending F inite Element

FINITE ELEMENT VERIFICATION -- PAGE NO. 4 * SUPPORT REACTIONS -UNIT KN METE STRUCTURE TYPE = SPACE ----------------JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 0.00 -18.91 -1.54 5.47 0.00 8 1 0.00 0.00 -112.19 0.00 11.56 0.00 15 1 0.00 0.00 -18.91 1.54 5.47 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 38. FINISH FINITE ELEMENT VERIFICATION -- PAGE NO. 5 * *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:36 **** ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ FINITE ELEMENT VERIFICATION -- PAGE NO. 6 * Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb

12 — STAAD.Pro

3 Deflection and Moments for a P late-Bending Finite Element

09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

13

3 Deflection and Moments for a Plate-Bending Finite Element

14 — STAAD.Pro

To find support reactions due to a load at the free end of a cantilever bent plate with an intermediate support.


Determine the reaction of the system as shown in the figure. Figure 4-1: Cantilever model

P = 1 kip L = 10 in

Verification Manual

15


Table 4-1: Comparison of reaction, in kips, for verification problem no. 4 Result Type

R

x

16 — STAAD.Pro

Theory

1.5

1.5

STAAD Basic Solver


1.5


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:40 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT INPUT FILE: ver04.STD 2. * FILE VER04.STD 3. * 4. * REFERENCE: 'STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO 5. * PAGE 346 PROBLEM NO. 2. THE ANSWER IN THE BOOK AFTER 6. * RECALCULATION = 1.5 7. * 8. UNIT INCH KIP 9. JOINT COORD 10. 1 0. 0. ; 2 0. 10. ; 3 0. 20. ; 4 10. 20. 11. SUPPORT 12. 1 FIXED ; 2 FIXED BUT FY MZ 13. MEMB INCI 14. 1 1 2 3 15. MEMB PROP ; 1 2 3 PRIS AX 10. IZ 100. 16. CONSTANT ; E 3000. ALL 17. LOADING 1 18. JOINT LOAD ; 4 FY -1. 19. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 8 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB :A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 2 * FILE VER04.STD 20. PRINT REACTION :A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 3 * FILE VER04.STD SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = PLANE ----------------JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 1.50 1.00 0.00 0.00 0.00 -5.00 2 1 -1.50 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 21. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:40 **** :A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 4 * FILE VER04.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 *

Verification Manual

17


* GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 5 * FILE VER04.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb

18 — STAAD.Pro



Verification Manual

19


20 — STAAD.Pro

To find deflections and stress at the center of a locomotive axle.

Timoshenko, S.,“Strength of Materials,” Part- 1, D. Van Nostrand Co., 3 rd edition, 1956. page 97, problems 1, 2.

Determine the maximum stress in a locomotive axle (as shown in the figure) as well as the deflection at the middle of the axle. Figure 5-1: Locomotive axle model

Diameter = 10 in., P = 26000 lbf E = 30E6 psi L1 = 13.5 in., L2 = 59 in.

Verification Manual

21


Table 5-1: Comparison of stress (σ), psi, and Deflection (δ), in. for verification model no. 5 Result Type

STAAD Basic Solver


σ

3575.*

3575.

3575.

δ

0.01040

0.01037

0.01037

* The value is recalculated.

22 — STAAD.Pro

Theory


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:46 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A LOCOMOTIVE AXLE INPUT FILE: ver05.STD 2. * FILE: VER05.STD 3. * 4. * REFERENCE 'STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO 5. * PAGE 97 PROBLEM NO. 1 AND 2. 6. * ANSWERS ARE 3580 FOR MAX. STRESS AND 0.104 INCH FOR MAX. DEFLN. 7. * 8. UNIT INCH POUND 9. JOINT COORD 10. 1 0. 0. ; 2 13.5 0. ; 3 43. 0. ; 4 72.5 0. ; 5 86. 0. 11. SUPPORT ; 2 4 PINNED 12. MEMB INCI ; 1 1 2 4 13. MEMB PROP ; 1 TO 4 TABLE ST PIPE OD 10. ID 0. 14. CONSTANT ; E 30E6 ALL 15. LOADING 1 16. JOINT LOAD ; 1 5 FY -26000. 17. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 5/ 4/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 4 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 11 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB 18. PRINT MEMBER STRESSES :A LOCOMOTIVE AXLE -- PAGE NO. 2 * FILE: VER05.STD :A LOCOMOTIVE AXLE -- PAGE NO. 3 * FILE: VER05.STD MEMBER STRESSES --------------ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 0.0 0.0 0.0 0.0 441.4 0.0 1.00 0.0 0.0 3575.3 3575.3 441.4 0.0 2 1 .0 0.0 0.0 3575.3 3575.3 0.0 0.0 1.00 0.0 0.0 3575.3 3575.3 0.0 0.0 3 1 .0 0.0 0.0 3575.3 3575.3 0.0 0.0 1.00 0.0 0.0 3575.3 3575.3 0.0 0.0 4 1 .0 0.0 0.0 3575.3 3575.3 441.4 0.0 1.00 0.0 0.0 0.0 0.0 441.4 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 19. PRINT DISPLACEMENTS :A LOCOMOTIVE AXLE -- PAGE NO. 4 * FILE: VER05.STD JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE -----------------JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 -0.01138 0.00000 0.00000 0.00000 0.00086 2 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00070 3 1 0.00000 0.01037 0.00000 0.00000 0.00000 0.00000

Verification Manual

23


4 1 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00070 5 1 0.00000 -0.01138 0.00000 0.00000 0.00000 -0.00086 ************** END OF LATEST ANALYSIS RESULT ************** 20. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:46 **** :A LOCOMOTIVE AXLE -- PAGE NO. 5 * FILE: VER05.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A LOCOMOTIVE AXLE -- PAGE NO. 6 * FILE: VER05.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb

24 — STAAD.Pro


01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

25


26 — STAAD.Pro

To find the maximum moment due to a uniform load on the horizontal member in a 1x1 bay plane frame.

McCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3 rd edition, 1975, page 383, example 22 - 5.

Determine the maximum moment in the frame. Figure 6-1: 1x1 bay plane frame

E and I same for all members. Verification Manual

27


Table 6-1: Comparison of moment, in kip-ft, for verification problem no. 6 Result Type

M

Max

28 — STAAD.Pro

Theory

44.40

STAAD Basic Solver

44.44


44.44


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:50 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A 1X1 BAY PLANE FRAME INPUT FILE: ver06.STD 2. * FILE VER06.STD 3. * 4. * REFERENCE: 'STRUCTURAL ANALYSIS' BY JACK C. MCCORMACK, 5. * PAGE 383 EXAMPLE 22-5, PLANE FRAME WITH NO SIDESWAY 6. * ANSWER - MAX BENDING = 44.4 FT-KIP 7. * 8. UNIT FT KIP 9. JOINT COORD 10. 1 0. 0. ; 2 0. 20. ; 3 20. 20. ; 4 20. 0. 11. MEMB INCI ; 1 1 2 3 12. MEMB PROP ; 1 2 3 PRIS AX 1. IZ 0.05 13. CONSTANT ; E 4132E3 ALL 14. SUPPORT ; 1 4 FIXED 15. LOADING 1 ; MEMB LOAD ; 2 UNI Y -2.0 16. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB 17. PRINT FORCES :A 1X1 BAY PLANE FRAME -- PAGE NO. 2 * FILE VER06.STD MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------ALL UNITS ARE -- KIP FEET (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 20.00 -3.33 0.00 0.00 0.00 -22.21 2 -20.00 3.33 0.00 0.00 0.00 -44.44 2 1 2 3.33 20.00 0.00 0.00 0.00 44.44 3 -3.33 20.00 0.00 0.00 0.00 -44.44 3 1 3 20.00 3.33 0.00 0.00 0.00 44.44 4 -20.00 -3.33 0.00 0.00 0.00 22.21 ************** END OF LATEST ANALYSIS RESULT ************** 18. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:50 **** :A 1X1 BAY PLANE FRAME -- PAGE NO. 3 * FILE VER06.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 *

Verification Manual

29


* GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A 1X1 BAY PLANE FRAME -- PAGE NO. 4 * FILE VER06.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb

30 — STAAD.Pro



Verification Manual

31


32 — STAAD.Pro

To find the joint deflection due to joint loads in a plane truss.


Determine the vertical deflection at point 5 of plane truss structure shown in the figure. Figure 7-1: Plane tru ss model

P = 20 kip Truss width = 4 spaces at 15 ft = 60 ft Truss height = 15 ft A

X 1-4

A

= 1 in2, A

X 9-11B

= 3

= 2 in2, A

X 5-6 2P in , A = X 12-13

4

X 7-8 in2

=1.5 in2,

E = 30E3 ksi

Verification Manual

33


Table 7-1: Comparison of deflection (δ) for verification problem no. 7 Result Type

δ (in.) 5

34 — STAAD.Pro

Theory

2.63

STAAD Basic Solver

2.63


2.63


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 4:55 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PLANE TRUSS INPUT FILE: ver07.STD 2. * FILE VER07.STD 3. * 4. * REFERENCE 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK, PAGE 271, 5. * EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH 6. * 8. UNIT FT KIP 9. JOINT COORD 10. 1 0 0 0 5 60 0 0 11. 6 15. 7.5 ; 7 30. 15. ; 8 45. 7.5 12. SUPPORT 13. 1 PINNED ; 3 FIXED BUT FX MZ 14. MEMB INCI 15. 1 2 6 ; 2 3 4 ; 3 4 8 ; 4 4 5 ; 5 1 2 16. 6 2 3 ; 7 3 6 ; 8 3 8 ; 9 3 7 17. 10 1 6 ; 11 5 8 ; 12 6 7 13 18. UNIT INCH 19. MEMB PROP 20. 1 TO 4 PRI AX 1.0 21. 5 6 PRIS AX 2. 22. 7 8 PRI AX 1.5 23. 9 10 11 PRI AX 3. 24. 12 13 PRI AX 4. 25. CONSTANT ; E 30E3 ALL 26. LOAD 1 VERTICAL LOAD 27. JOINT LOAD 28. 2 4 5 FY -20.0 29. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. :A PLANE TRUSS -- PAGE NO. 2 * FILE VER07.STD P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 8/ 13/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 5/ 5/ 11 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 13 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB 30. PRINT DISPLACEMENTS LIST 5 :A PLANE TRUSS -- PAGE NO. 3 * FILE VER07.STD JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS -----------------JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 5 1 -0.72000 -2.63033 0.00000 0.00000 0.00000 0.00000 ************** END OF LATEST ANALYSIS RESULT ************** 31. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 4:55 **** :A PLANE TRUSS -- PAGE NO. 4 * FILE VER07.STD ************************************************************

Verification Manual

35


* For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A PLANE TRUSS -- PAGE NO. 5 * FILE VER07.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb

36 — STAAD.Pro


11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

37


38 — STAAD.Pro

To find the maximum moment due to a concentrated load on the horizontal member in a 1x1 bay plane frame.

McCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3 rd edition, 1975, page 385, problem 22 - 6.

Determine the maximum moment in the structure. Figure 8-1: Unequal leg bay model

P = 30 kip H1 = 20 ft, H3 = 30 ft L = 30 ft, with P occurring at 10 ft from Leg #1 E and I same for all members

Verification Manual

39


Table 8-1: Comparison of max. moment, in kip-ft, for verification model no. 8 Result Type

M

Max

40 — STAAD.Pro

Theory

69.40

STAAD Basic Solver

69.44


69.44


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5: 0 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A 1X1 BAY PLANE FRAME INPUT FILE: ver08.STD 2. * FILE VER08.STD 3. * 4. * REFERENCE: 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK, 5. * PAGE 385 PROB 22-6. 6. * ANSWER - MAX BENDING IN MEMB 1 = 69.4 KIP-FT 7. * 8. UNIT FT KIP 9. JOINT COORD 10. 1 0. 10. ; 2 0 30 ; 3 30 30 ; 4 30 0 11. SUPPORT ; 1 4 FIXED 12. MEMB INCI 13. 1 1 2 3 14. MEMB PROP ; 1 2 3 TAB ST W12X26 15. CONSTANT ; E 4176E3 16. LOAD 1 VERTICAL LOAD 17. MEMBER LOAD 18. 2 CON Y -30. 10. 19. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB :A 1X1 BAY PLANE FRAME -- PAGE NO. 2 * FILE VER08.STD 20. PRINT FORCES :A 1X1 BAY PLANE FRAME -- PAGE NO. 3 * FILE VER08.STD MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------ALL UNITS ARE -- KIP FEET (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 20.09 -3.74 0.00 0.00 0.00 -5.34 2 -20.09 3.74 0.00 0.00 0.00 -69.44 2 1 2 3.74 20.09 0.00 0.00 0.00 69.44 3 -3.74 9.91 0.00 0.00 0.00 -66.66 3 1 3 9.91 3.74 0.00 0.00 0.00 66.66 4 -9.91 -3.74 0.00 0.00 0.00 45.51 ************** END OF LATEST ANALYSIS RESULT ************** 21. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5: 0 **** :A 1X1 BAY PLANE FRAME -- PAGE NO. 4 * FILE VER08.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * *

Verification Manual

41


* Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A 1X1 BAY PLANE FRAME -- PAGE NO. 5 * FILE VER08.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb

42 — STAAD.Pro


02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

43


44 — STAAD.Pro

To find the maximum moment due to lateral joint loads in a 1x2 bay plane frame.


Determine the maximum moment in the frame. Figure 9-1: Two story f rame model

L = 20 ft H3 = 20 kip, H5 = 10 kip E and I same for all members. Verification Manual

45


Table 9-1: Comparison of max. moment, in kip-ft, for verification problem no. 9 Result Type

M

Max

46 — STAAD.Pro

Theory

176.40

STAAD Basic Solver

178.01


178.01


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5: 6 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A 1X2 BAY PLANE FRAME INPUT FILE: ver09.STD 2. * FILE: VER09.STD 3. * 4. * REFERENCE: 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK, 5. * PAGE 388, PROB 22-7. 6. * ANSWER - MAX MOM IN MEMB 1 = 176.4 K-F 7. * 8. UNIT FT KIP 9. JOINT COORD 10. 1 0 0 0 5 0 40 0 2 ; 2 20 0 0 6 20 40 0 2 11. SUPPORT ; 1 2 FIXED 12. MEMB INCI 13. 1 1 3 2 ; 3 3 5 4 ; 5 3 4 ; 6 5 6 14. MEMB PROP 15. 1 TO 6 PRI AX .2 IZ .1 16. CONSTANT ; E 4176E3 17. LOAD 1 HORIZONTAL LOAD 18. JOINT LOAD 19. 3 FX 20 ; 5 FX 10 20. PERFORM ANALYS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 6/ 6/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 3/ 3/ 9 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 12 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB :A 1X2 BAY PLANE FRAME -- PAGE NO. 2 * FILE: VER09.STD 21. PRINT FORCES :A 1X2 BAY PLANE FRAME -- PAGE NO. 3 * FILE: VER09.STD MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------ALL UNITS ARE -- KIP FEET (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 -22.26 15.06 0.00 0.00 0.00 178.01 3 22.26 -15.06 0.00 0.00 0.00 123.16 2 1 2 22.26 14.94 0.00 0.00 0.00 176.73 4 -22.26 -14.94 0.00 0.00 0.00 122.10 3 1 3 -6.51 4.97 0.00 0.00 0.00 34.49 5 6.51 -4.97 0.00 0.00 0.00 64.93 4 1 4 6.51 5.03 0.00 0.00 0.00 35.34 6 -6.51 -5.03 0.00 0.00 0.00 65.24 5 1 3 9.91 -15.75 0.00 0.00 0.00 -157.65 4 -9.91 15.75 0.00 0.00 0.00 -157.44 6 1 5 5.03 -6.51 0.00 0.00 0.00 -64.93 6 -5.03 6.51 0.00 0.00 0.00 -65.24 ************** END OF LATEST ANALYSIS RESULT ************** 22. FINISH *********** END OF THE STAAD.Pro RUN ***********

Verification Manual

47


**** DATE= MAR 9,2011 TIME= 11: 5: 6 **** :A 1X2 BAY PLANE FRAME -- PAGE NO. 4 * FILE: VER09.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A 1X2 BAY PLANE FRAME -- PAGE NO. 5 * FILE: VER09.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb

48 — STAAD.Pro


01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

49


50 — STAAD.Pro

To find the maximum axial force and moment due to load and moment applied at a joint in a Space frame.

Weaver Jr., W., “Computer Programs for Structural Analysis,” page 146, problem 8.

Determine the maximum axial force and m oment in the space structure. Figure 10-1: Space frame model

F = 2 kip, P = 1 kip, M = 120 in·kip L = 120 in. E = 30E3 ksi, AX = 11 in 2 IX = 83 in 4 IY = 56 in 4 IZ = 56 in4

Verification Manual

51


Table 10-1: Comparison of max. Force, F, and max. Moments,M, for verification problem no. 10 Result Type

F

Max

(kips)

STAAD Basic Solver


1.47

1.47

1.47

M

(in·kip)

84.04

84.04

84.04

M

(in·kip)

95.319

96.120

96.120

Y,Max Z,Max

52 — STAAD.Pro

Theory


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:12 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE :A SPACE FRAME INPUT FILE: ver10.STD 2. * FILE VER10.STD 3. * 4. * REFERENCE 'COMPUTER PROGRAMS FOR STRUCTURAL ANALYSIS' 5. * BY WILLIAM WEAVER JR. PAGE 146 STRUCTURE NO. 8. 6. * ANSWER - MAX AXIAL FORCE= 1.47 (MEMB 3) 7. * MAX BEND-Y= 84.04 (MEMB 3), BEND-Z= 95.32 (MEMB 3) 8. * 9. * STAAD VERIFICATION PROB NO. 10 10. * 11. UNIT INCH KIP 12. JOINT COORD 13. 1 0 120 0 ; 2 240 120 0 14. 3 0 0 0 ; 4 360 0 120 15. SUPPORT 16. 3 4 FIXED 17. MEMB INCI 18. 1 1 2 ; 2 3 1 ; 3 2 4 19. MEMB PROP 20. 1 2 3 PRIS AX 11. IX 83. IY 56. IZ 56 21. CONSTANT ; E 30000. ALL 22. POISS .25 ALL 23. LOAD 1 JOINT LOAD 24. JOINT LOAD 25. 1 FX 2. ; 2 FY -1. ; 2 MZ -120. 26. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2 :A SPACE FRAME -- PAGE NO. * FILE VER10.STD SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 2/ 2/ 12 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 12 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB 27. PRINT ANALYSIS RESULT :A SPACE FRAME -- PAGE NO. * FILE VER10.STD JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE -----------------JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.22267 0.00016 -0.17182 -0.00255 0.00217 -0.00213 2 1 0.22202 -0.48119 -0.70161 -0.00802 0.00101 -0.00435 3 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 :A SPACE FRAME -- PAGE NO. * FILE VER10.STD SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = SPACE ----------------JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 3 1 -1.10 -0.43 0.22 48.78 -17.97 96.12 4 1 -0.90 1.43 -0.22 123.08 47.25 -11.72 :A SPACE FRAME -- PAGE NO.

2

3

4

5

Verification Manual

53


* FILE VER10.STD MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------ALL UNITS ARE -- KIP INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 0.90 -0.43 0.22 22.71 -17.97 -36.37 2 -0.90 0.43 -0.22 -22.71 -34.18 -67.36 2 1 3 -0.43 1.10 0.22 -17.97 -48.78 96.12 1 0.43 -1.10 -0.22 17.97 22.71 36.37 3 1 2 1.47 -0.71 -0.48 -37.02 15.69 -53.28 4 -1.47 0.71 0.48 37.02 84.04 -95.32 ************** END OF LATEST ANALYSIS RESULT ************** 28. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:12 **** :A SPACE FRAME -- PAGE NO. 6 * FILE VER10.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A SPACE FRAME -- PAGE NO. 7 * FILE VER10.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb

54 — STAAD.Pro


09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

55


56 — STAAD.Pro

A rigid bar is suspended by two copper wires and one steel wire. Find the stresses in the wires due to a rise in temperature.

Timoshenko, S., “Strength of Materials,” Part 1, D. Van Nostrand Co., 3rd edition, 1956, page 30, problem 9.

Assuming the horizontal member to be very rigid, determine the stresses in the copper and steel wires if the temperature rise is 10º F. Figure 11-1: Model of a rigid wire suspended by wires

E

steel

α

steel

= 30E6 psi, E

copper

= 16E6 psi

= 70E-7 in/in/°F, α

copper

= 92E-7 in/in/°F

A = 0.1 in2 X

w = 400 lbf/in. L = 20 in. d= 5 in.

Verification Manual

57


Hint: When

modeling, assume a large moment of inertia for the h orizontal rigid member and distribute of the concentrated load as uniform.

Table 11-1: Comparison of stress (σ) for verification model #11 Result Type

σ

Steel

σ

(psi)

Copper

58 — STAAD.Pro

(psi)

Theory

STAAD Basic Solver


19,695

19,698

19,698

10,152

10,151

10,151


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:17 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL WIRE INPUT FILE: ver11.STD 2. * FILE: VER11.STD 3. * 4. * REFERENCE: 'STRENGTH OF MATERIALS', TIMOSHENKO (PART 1), 5. * PAGE 30, PROB 9. 6. * THE ANSWERS ARE 19700 PSI AND 10200 PSI. 7. * 8. UNIT INCH POUND 9. JOINT COORD 10. 1 0. 20. ; 2 5. 20. ; 3 10. 20. 11. 4 0. 0. ; 5 5. 0. ; 6 10. 0. 12. MEMB INCI 13. 1 1 4 3 ; 4 4 5 5 14. MEMB PROP 15. 1 2 3 PRI AX 0.1 ; 4 5 PRI AX 1. IZ 100. 16. CONSTANT ; E 30E6 MEMB 2 4 5 17. E 16E6 MEMB 1 3 18. ALPHA 92E-7 MEMB 1 3 ; ALPHA 70E-7 MEMB 2 19. MEMB TRUSS ; 1 2 3 20. SUPPORT ; 1 2 3 PINNED 21. LOADING 1 VERT LOAD + TEMP LOAD 22. MEMB LOAD ;4 5 UNI Y -400. 23. TEMP LOAD ; 1 2 3 TEMP 10. 24. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. :A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 2 * FILE: VER11.STD P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 6/ 5/ 3 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 3/ 3/ 10 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 12 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB ZERO STIFFNESS IN DIRECTION 6 AT JOINT 1 EQN.NO. 1 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. ZERO STIFFNESS IN DIRECTION 6 AT JOINT 2 EQN.NO. 2 ZERO STIFFNESS IN DIRECTION 6 AT JOINT 3 EQN.NO. 3 ***WARNING - INSTABILITY AT JOINT 6 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 6.0000004E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 10 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. 25. PRINT STRESSES LIST 1 2 3

Verification Manual

59


:A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 3 * FILE: VER11.STD MEMBER STRESSES --------------ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 10150.8 T 0.0 0.0 10150.8 0.0 0.0 1.00 10150.8 T 0.0 0.0 10150.8 0.0 0.0 2 1 .0 19698.3 T 0.0 0.0 19698.3 0.0 0.0 1.00 19698.3 T 0.0 0.0 19698.3 0.0 0.0 3 1 .0 10150.8 T 0.0 0.0 10150.8 0.0 0.0 1.00 10150.8 T 0.0 0.0 10150.8 0.0 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 26. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:18 **** :A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 4 * FILE: VER11.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ :A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 5 * FILE: VER11.STD Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb

60 — STAAD.Pro


06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

61


62 — STAAD.Pro

To find the joint deflection and member stress due to a joint load in a plane truss.


Determine the vertical deflection at point A and the member stresses Figure 12-1: Model Model of two member member truss

A = 0.5 in2 X

E = 30E6 psi P = 5000 lbf L = 180 in. angle = 30°

Verification Manual

63

12 Deflection and stress of a truss system

Table 12-1: Comparison of stress (σ) and Deflection (δ) for verification problem 12 Res Result Typ Type

STAAD Basic Solver


σ (psi)

10,000.

10,000.

10,000.

δ (i n )

0.12

0.12

0.12

A A

64 — STAAD.Pro

The Theory


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:23 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PLANE TRUSS INPUT FILE: ver12.STD 2. * FILE VER12.STD 3. * 4. * REFERENCE: 'STRENGTH OF MATERIALS', (PART 1) BY TIMOSHENKO, 5. * PAGE 10, PROB 2. 6. * 7. * THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH 8. * AND STRESS =10000 PSI 9. * 10. UNIT INCH POUND 11. JOINT COORD 12. 1 0. 0. ; 2 155.88457 -90. ; 3 311.76914 0. 13. SUPPORT ; 1 3 PINNED 14. MEMB INCI ; 1 1 2 2 15. MEMB PROP 16. 1 2 PRIS AX 0.5 17. CONSTANT ; E 30E6 18. LOAD 1 VERT LOAD 19. JOINT LOAD ; 2 FY -5000. 20. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 3/ 2/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 2 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2 SIZE OF STIFFNESS MATRIX = 0 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB :A PLANE TRUSS -- PAGE NO. 2 * FILE VER12.STD 21. PRINT DISPLACEMENTS LIST 2 :A PLANE TRUSS -- PAGE NO. 3 * FILE VER12.STD JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS -----------------JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 2 1 0.00000 -0.12000 0.00000 0.00000 0.00000 0.00000 ************** END OF LATEST ANALYSIS RESULT ************** 22. PRINT STRESSES :A PLANE TRUSS -- PAGE NO. 4 * FILE VER12.STD MEMBER STRESSES --------------ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 10000.0 T 0.0 0.0 10000.0 0.0 0.0 1.00 10000.0 T 0.0 0.0 10000.0 0.0 0.0 2 1 .0 10000.0 T 0.0 0.0 10000.0 0.0 0.0 1.00 10000.0 T 0.0 0.0 10000.0 0.0 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 23. FINISH *********** END OF THE STAAD.Pro RUN ***********

Verification Manual

65


**** **** DAT DATE= E= MAR MAR 9,20 9,2011 11 TIME TIME= = 11: 11: 5:23 5:23 *** **** * :A PLANE TRUSS -- PAGE NO. 5 * FILE VER12.STD VER12.STD ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +3 +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN JAPAN +81 +81 (03) (03)59 5952 52-6 -650 500 0 http http:/ ://w /www ww.c .ctc tc-g -g.c .co. o.jp jp * * CHINA +86 21 6288 4040 * * THAILAND THAILAND +66 (0)2645-1 (0)2645-1018/ 018/19 19 partha.p@r partha.p@reis eisoftw oftwaret areth.c h.com* om* * * * World Worldwid wide e http: http:// //sel selec ectse tserv rvic ices. es.be bentl ntley ey.c .com/ om/en en-U -US/ S/ * * * ************************************************************ :A PLANE TRUSS -- PAGE NO. 6 * FILE VER12.STD VER12.STD Informat Information ion about about the key files files in the current current distributi distribution on Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/ 06/05/200 2007 0xbc00 c00 003317 31776 aiscsect ections_a s_all_edit ditions.m s.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/ 06/28/200 2005 0x8201 201 003276 27680 butlerco rcoldform ormedsect ections.m s.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb

66 — STAAD.Pro


01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/ 02/21/200 2008 0xc380 380 003276 27680 Jap JapaneseC seColdFo dFormedSe dSections ons.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/ 11/09/200 2005 0x9081 081 003768 76832 Kin Kingspanc ancoldfo dformedse dsections ons.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/ 04/24/200 2007 0x99c0 9c0 001146 14688 lys lysaghtco tcoldfor formedsec sections. ns.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

67


68 — STAAD.Pro

Steel Design.

Attached step by step hand calculation as per 1989 AISC ASD code. Ninth Edition.

Determine the allowable stresses (per 1989 AISC code) for the members of the structure as shown in figure. Also, perform a code check for these members based on the results of the analysis. Figure 13-1: Steel braced frame frame

Members 1, 2 = W12X26, Members 3, 4 = W14X43 Members 5, 6, 7 = W16X36, Memb 8= L40404, Memb 9 = L50506 F = 15 kip (wind load) w = 2 kip/ft (dead load + liveload)

Verification Manual

69


Table 13-1: Comparison of governing ratios for the member checks in verification problem no. 13 Member No.

1

2

3

4

5

6

7

8

9

Hand Calculation

1.1576 .914 1.117 0.936 .579 1.119

.668 1.024 .823

STAAD Basic Solver

1.157

.916 1.117 0.936 .582 1.120 .668 1.024 .823


1.157

.916 1.117 0.936 .582 1.120 .668 1.024 .823

Manual / Code refers to AISC Manual of Steel Construction, Allowable Stress Design, ninth edition.

Size W12x26, L = 10 ft., a = 7.65 in 2, Sz = 33.39 in 3 From clause F1-2, page 5-45 of Manual, L = 6.85 ft. c

From observation Load case 1 will govern, F = 25.0 kip (compression), M = 56.5 ft·kip x

z

Area of compressive flange = 6.49*0.38 = 2.466 in2 Allowable bending stress, per Clause F1-8 (page 5-47 of Manual) f = 12. · 1000 · 1.0/[10 · 12 · (12.22/2.466)] = 20.1817 ksi b

(kl/r)y = 120/1.5038 = 79.8, so f = 15.38 ksi a

Stresses per Table C-36 (page 3-16 of manual) f = 25./7.65 = 3.268 a

f = 56.5 · 12/33.39 = 20.31 ksi b

(kl/r)z = 120/5.1639 = 23.238, so F' = = 276.54 ksi ez

Equation H1-1, page 5-54 of Manual 3.268/15.38 + 0.85 · 20.31 / [(1-3.268/276.54) · 20.1817] = 1.078 Equation H1-2, page 5-54 of Manual. 3.268/(0.6 · 36) +20.31/20.1817 = 1.1576 Therefore, equation H1-2 governs and ratio = 1.1576

Size W12x26, L = 5 ft., a = 7.65 in 2, Sz = 33.39 in 3 From observation load case 1 will govern, F = 8.71 kip (compression), M = 56.50 ft·kip x

70 — STAAD.Pro

z


Since L is less than L = 6.85ft, per Clauses F1-1 & F1-2 (page 5-45 of Manual) c

f = 0.66 · 36 = 23.76 ksi b

(kl/r)y = 60/1.5038 = 39.90, so f = 19.19 ksi a

Per Table C-36 (page 3-16 of Manual) f = 8.71/7.65 = 1.1385, f = 56.5 · 12/33.39 = 20.31 ksi a

b

Since f /F less than 0.15, apply equation H1-3 (page 5-54 of Manual) a

a

1.1385/19.19 + 20.31/23.76 = .0593 + .8548 = 0.9141

Size W14X43, L = 11ft., a = 12.6 in 2, Sz = 62.7 in 3 From observation load case 3 will govern, F = 25.5 kip (compression), M = 112.173 ft·kip x

z

Referring to clause F1-2, page 5-45 of Manual. L = 8.4 ft. Therefore c

f = 0.6 · 36 = 21.6 ksi b

(kl/r)y = 132/1.8941 = 69.69, so f = 16.46 ksi per Table C-36 (page 3-16 of Manual) a

f = 25.5/12.6 = 2.024 a

f = 112.173 · 12/62.66 = 21.48 ksi b

since f /F less than 0.15, use equation H1-3, page 5-54 of Manual a

a

2.024/16.46 + 21.48/21.6 = 0.123 + 0.994 = 1.117

Size W14x43, L = 4ft, a = 12.6 in 2, Sz = 62.7 in 3 From observation, load case 3 will govern, F = 8.75 kip (tension), M = 112.173 ft·kip x

z

Since L is less than L = 8.4 ft c

f = 0.66 · 36 = 23.76 ksi b

Clause F1-1 (page 5-45 of Manual) f = 8.75/12.6 = 0.694 a

f = 112.73x12/62.66 = 21.48 ksi b

Combined tension and bending, use equation H2-1, page 5-55 of Manual. 0.694/(0.6 · 36) + 21.48/23.76 = 0.032 + 0.904 = 0.936

Size W16x36, L = 5ft, a = 10.6 in 2, Sz = 56.49 in 3 From observation, load case 3 will govern. Verification Manual

71


F = 14.02 kip (compression), M =57.04 ft·kip x

z

Since L is less than L = 7.37 (per Clause F1-2, page 5-45 of Manual) c

f = 0.66 · 36 = 23.76 ksi b

(kl/r)y = 60./1.52 = 39.47 so f = 19.23 ksi per Table C-36 (page 3-16 of Manual) a

f = 14.02/10.6 = 1.32 a

f = 57.04 · 12/56.5 = 12.12 ksi b

Since f /F less than 0.15, use equation H1-3, page 5-54 of Manual a

a

1.32/19.23 + 12.12/23.76 = 0.069 + 0.510 = 0.579

Size W16x36, L = 16ft, a = 10.6 in 2, Sz = 56.49 in 3 From observation, load case 1 will govern. Forces at midspan are F = 5.65 kip (compression), M = 71.25 ft·kip x

z

From Chapter F of the AISC ASD 9P thP ed. specs., with Cb = 1.0, (102,000Cb/Fy)1/2 =53.229 (510,000Cb/Fy)1/2 =119.02 L/rT = 192/1.79 = 107.26 53.229 < 107.26 < 119.02 Therefore F (as per F1-6, page 5-47 of Manual) b

[(2/3) – 36 · 107.26 · 107.26/(1,530,000)] · 36 = 14.25 ksi (Kl/r)y = 192/1.5203 = 126.29 so f = 9.36 per Table C-36 (page 3-16 of Manual) a

f = 5.65/10.6 = 0.533 a

f = 71.25x12/56.49 = 15.14 ksi b

Since f /F less than 0.15 use formula [H1-3, page 5-54 of Manual] a

a

0.533/9.36 + 15.14/14.25 = 0.057 + 1.062 = 1.119

Size W16x36, L =4ft, a = 10.6in 2, Sz =56.49in 3 L = 7.37ft (Clause F1-2 page 5-45 of Manual) c

From observation load case 3 will govern, F = 24.06 kip (tension), M = 62.96 ft·kip x

From Clause F1-1, the allowable compressive stress is f = 0.66 Fy = 23.76 ksi b

Since section is in tension, per Clause F1-5 (page5-45 of Manual) f = 0.60 · 36 = 21.60 Ksi b

72 — STAAD.Pro

z


Choosing the larger of above 2 values, f = 23.76 Ksi b

f = 24.06/10.6 = 2.2698 a

f = 62.96 · 12/56.49 = 13.37 b

Since combined tension and bending, use equation H 2-1, page 5-55 of the AISC ASD 9PthP ed. specs. 2.2698/(0.6 · 36) + 13.37(23.76) = 0.105 + 0.5627 = 0.6677

Size L4x4x1/4, L = 7.071 ft, a = 1.94 in 2 From observation load case 1 will govern, F = 23.04 kip (Comp.) x

Fa is computed as per page 5-310 of the AISC ASD 9P thP ed.specs. Q = 1.34 – 0.00447 · (4/0.25)·(36)1/2 = 0.9108 s

Q = 1.0 a

Q = Q · Q = 0.9108 s

a 2 C = 92.0·π ·E/(Q·F )]1/2 = [2.0·π 2 c y

· 29000/(0.9108 · 36)] 1/2 = 132.1241

Kl/r = 7.071 · 12/0.795 = 106.73 < C . c

Hence, f = 11.6027 ksi (computed per equation 4-1) a

Actual compressive stress f = 23.04/1.94 = 11.876 ksi a

Therefore, Ratio = f /f = 11.876/11.602 = 1.024 a a

Size L5x5x3/8, L = 5.657 ft, a = 3.61 in 2 From observation, load case 1 governs, F = 48.44 kip (Comp.) x

Fa is computed as per page 5-310 of the AISC ASD 9P thP ed.specs. Q = 1.34 – 0.00447 · (5/0.375)·(36)1/2 = 0.9824 s

Q = 1.0 a

Q = Q · Q = 0.9824 s

a 2 C = 92.0·π ·E/(Q·F )]1/2 = [2.0·π 2 c y

· 29000/(0.9824 · 36)] 1/2 = 127.2238

(Kl/r)min = 5.657 · 12/0.99 = 68.57 < C . c

Hence, f = 16.301 ksi (computed per equation 4-1) a

Actual compressive stress f = 48.44/3.61 = 13.418 ksi a

Therefore Ratio = f /f = 13.418/16.301 = 0.823 a a

Verification Manual

73


74 — STAAD.Pro


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:28 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE VERIFICATION PROBLEM NO 13 INPUT FILE: ver13.STD 2. * 3. * THIS DESIGN EXAMPLE IS VERIFIED BY HAND CALCULATION 4. * FOLLOWING AISC-89 CODE. 5. * 6. UNIT FEET KIP 7. JOINT COORD 8. 1 0 0 ; 2 25 0 ; 3 0 10 ; 4 25 11 9. 5 0 15 ; 6 25 15 ; 7 5 15 ; 8 21 15 10. MEMB INCI 11. 1 1 3 ; 2 3 5 ; 3 2 4 ; 4 4 6 12. 5 5 7 ; 6 7 8 ; 7 8 6 ; 8 3 7 ; 9 4 8 13. MEMB PROP AMERICAN 14. 1 2 TA ST W12X26 ; 3 4 TA ST W14X43 15. 5 6 7 TA ST W16X36 ; 8 TA ST L40404 ; 9 TA ST L50506 16. MEMB TRUSS ; 8 9 17. CONSTANT 18. E 4176E3 ALL 19. POISSON STEEL ALL 20. SUPPORT ; 1 2 PINNED 21. LOADING 1 DL + LL 22. MEMB LOAD ; 5 6 7 UNI Y -2.0 23. LOADING 2 WIND FROM LEFT 24. JOINT LOAD ; 5 FX 15. 25. LOAD COMB 3 ; 1 0.75 2 0.75 26. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 8/ 9/ 2 VERIFICATION PROBLEM NO 13 -- PAGE NO. 2 * SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 4/ 4/ 15 DOF TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 20 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB 27. LOAD LIST 1 3 28. PRINT FORCES VERIFICATION PROBLEM NO 13 -- PAGE NO. 3 * MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------ALL UNITS ARE -- KIP FEET (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 25.00 -5.65 0.00 0.00 0.00 0.00 3 -25.00 5.65 0.00 0.00 0.00 -56.50 3 1 12.00 1.05 0.00 0.00 0.00 0.00 3 -12.00 -1.05 0.00 0.00 0.00 10.52 2 1 3 8.71 10.64 0.00 0.00 0.00 56.50 5 -8.71 -10.64 0.00 0.00 0.00 -3.29 3 3 15.83 -2.77 0.00 0.00 0.00 -10.52 5 -15.83 2.77 0.00 0.00 0.00 -3.34 3 1 2 25.00 5.65 0.00 0.00 0.00 0.00 4 -25.00 -5.65 0.00 0.00 0.00 62.15

Verification Manual

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3

2 25.50 10.20 0.00 0.00 0.00 0.00 4 -25.50 -10.20 0.00 0.00 0.00 112.17 4 1 4 6.50 -12.85 0.00 0.00 0.00 -62.15 6 -6.50 12.85 0.00 0.00 0.00 10.76 3 4 -8.75 -24.06 0.00 0.00 0.00 -112.17 6 8.75 24.06 0.00 0.00 0.00 15.95 5 1 5 -10.64 8.71 0.00 0.00 0.00 3.29 7 10.64 1.29 0.00 0.00 0.00 15.25 3 5 14.02 15.83 0.00 0.00 0.00 3.34 7 -14.02 -8.33 0.00 0.00 0.00 57.04 6 1 7 5.65 15.00 0.00 0.00 0.00 -15.25 8 -5.65 17.00 0.00 0.00 0.00 -0.75 3 7 10.20 4.50 0.00 0.00 0.00 -57.04 8 -10.20 19.50 0.00 0.00 0.00 -62.96 7 1 8 -12.85 1.50 0.00 0.00 0.00 0.75 6 12.85 6.50 0.00 0.00 0.00 -10.76 3 8 -24.06 14.75 0.00 0.00 0.00 62.96 6 24.06 -8.75 0.00 0.00 0.00 -15.95 8 1 3 23.04 0.00 0.00 0.00 0.00 0.00 7 -23.04 0.00 0.00 0.00 0.00 0.00 3 3 -5.41 0.00 0.00 0.00 0.00 0.00 7 5.41 0.00 0.00 0.00 0.00 0.00 9 1 4 26.16 0.00 0.00 0.00 0.00 0.00 8 -26.16 0.00 0.00 0.00 0.00 0.00 3 4 48.44 0.00 0.00 0.00 0.00 0.00 8 -48.44 0.00 0.00 0.00 0.00 0.00 VERIFICATION PROBLEM NO 13 -- PAGE NO. 4 * ************** END OF LATEST ANALYSIS RESULT ************** 29. PARAMETER 30. CODE AISC 31. TRACK 1.0 ALL 32. CHECK CODE ALL VERIFICATION PROBLEM NO 13 -- PAGE NO. 5 * STAAD.Pro CODE CHECKING - (AISC 9TH EDITION) v1.0 *********************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE NOTED) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= * 1 ST W12X26 (AISC SECTIONS) FAIL AISC- H1-2 1.157 1 25.00 C 0.00 56.50 10.00 ----------------------------------------------------------------------| MEM= 1, UNIT KIP-INCH, L= 120.0 AX= 7.65 SZ= 33.4 SY= 5.3| | KL/R-Y= 79.8 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 20.18 | | FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 15.26 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------2 ST W12X26 (AISC SECTIONS) PASS AISC- H1-3 0.916 1 8.71 C 0.00 56.50 0.00 ----------------------------------------------------------------------| MEM= 2, UNIT KIP-INCH, L= 60.0 AX= 7.65 SZ= 33.4 SY= 5.3| | KL/R-Y= 39.9 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.61 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------* 3 ST W14X43 (AISC SECTIONS) FAIL AISC- H1-3 1.117 3 25.50 C 0.00 -112.17 11.00 ----------------------------------------------------------------------| MEM= 3, UNIT KIP-INCH, L= 132.0 AX= 12.60 SZ= 62.7 SY= 11.3| | KL/R-Y= 69.7 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 21.60 | | FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 16.46 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------4 ST W14X43 (AISC SECTIONS)

76 — STAAD.Pro


PASS AISC- H2-1 0.936 3 8.75 T 0.00 -112.17 0.00 ----------------------------------------------------------------------| MEM= 4, UNIT KIP-INCH, L= 48.0 AX= 12.60 SZ= 62.7 SY= 11.3| | KL/R-Y= 25.3 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 20.26 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------5 ST W16X36 (AISC SECTIONS) PASS AISC- H1-3 0.582 3 14.02 C 0.00 -57.04 5.00 VERIFICATION PROBLEM NO 13 -- PAGE NO. * ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE NOTED) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= ----------------------------------------------------------------------| MEM= 5, UNIT KIP-INCH, L= 60.0 AX= 10.60 SZ= 56.5 SY= 7.0| | KL/R-Y= 39.5 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.39 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------* 6 ST W16X36 (AISC SECTIONS) FAIL AISC- H1-3 1.120 1 5.65 C 0.00 -71.25 8.00 ----------------------------------------------------------------------| MEM= 6, UNIT KIP-INCH, L= 192.0 AX= 10.60 SZ= 56.5 SY= 7.0| | KL/R-Y= 126.3 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 14.24 | | FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 9.36 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------7 ST W16X36 (AISC SECTIONS) PASS AISC- H2-1 0.668 3 24.06 T 0.00 62.96 0.00 ----------------------------------------------------------------------| MEM= 7, UNIT KIP-INCH, L= 48.0 AX= 10.60 SZ= 56.5 SY= 7.0| | KL/R-Y= 31.6 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.87 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------* 8 ST L40404 (AISC SECTIONS) FAIL AISC- H1-1 1.024 1 23.04 C 0.00 0.00 0.00 ----------------------------------------------------------------------| MEM= 8, UNIT KIP-INCH, L= 84.9 AX= 1.94 SZ= 0.8 SY= 1.7| | KL/R- = 106.7 CB= 0.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 0.00 | | FTZ= 0.00 FCY= 0.00 FTY= 0.00 FC= 11.60 FT= 21.60 FV= 0.00 | ----------------------------------------------------------------------9 ST L50506 (AISC SECTIONS) PASS AISC- H1-1 0.823 3 48.44 C 0.00 0.00 0.00 ----------------------------------------------------------------------| MEM= 9, UNIT KIP-INCH, L= 67.9 AX= 3.61 SZ= 1.8 SY= 3.9| | KL/R- = 69.0 CB= 0.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 0.00 | | FTZ= 0.00 FCY= 0.00 FTY= 0.00 FC= 16.30 FT= 21.60 FV= 0.00 | ----------------------------------------------------------------------VERIFICATION PROBLEM NO 13 -- PAGE NO. * 33. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:28 **** ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 *

6

7

Verification Manual

77


* FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ VERIFICATION PROBLEM NO 13 -- PAGE NO. 8 * Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb

78 — STAAD.Pro


01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

Verification Manual

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80 — STAAD.Pro

Concrete design as per ACI code.

CRSI Handbook and Notes on ACI-318-99.

A plane frame is created with such loading as to create 138 Kip-Ft moment on beam and 574 Kip of axial load coupled with above moment on column. Figure 14-1: Concrete moment frame

Size of the beam is 10" x 16"and size of the column 14" x 16". P = 521.32 kip w = 5.268 kip/ft L = 20 ft, H = 15 ft Verification Manual

81


Table 14-1: Comparison of concrete designs for verifcation problem no. 14 Result Type

82 — STAAD.Pro

Theory ACI Notes

Theory CRSI Handbook

STAAD Basic Solver


Area of Steel in beam

2.78 in2

X

2.792 in 2

2.792 in2

Area of Steel in column

X

4.01%

4.09% required

4.09% required

4.23% provided

4.23% provided


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:33 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE VERIFICATION FOR CONCRETE DESIGN INPUT FILE: ver14.STD 2. UNIT KIP FEET 3. JOINT COORDINATES 4. 1 0. 0. ; 2 0. 15. ; 3 20. 15. ; 4 20. 0. 5. MEMBER INCIDENCE 6. 1 1 2 ; 2 2 3 ; 3 3 4 7. UNIT INCH 8. MEMBER PROPERTY 9. 1 3 PRISMATIC YD 16. ZD 14. 10. 2 PRISM YD 16. ZD 10. 11. CONSTANTS 12. E CONCRETE ALL 13. POISSON CONCRETE ALL 14. SUPPORT 15. 1 4 FIXED 16. UNIT FT 17. LOADING 1 DEAD + LIVE 18. JOINT LOAD 19. 2 3 FY -521.32 20. MEMBER LOAD 21. 2 UNI GY -5.268 22. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 2 23. PRINT MEMBER FORCES VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 3 MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------ALL UNITS ARE -- KIP FEET (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 574.00 -13.69 0.00 0.00 0.00 -67.44 2 -574.00 13.69 0.00 0.00 0.00 -137.87 2 1 2 13.69 52.68 0.00 0.00 0.00 137.87 3 -13.69 52.68 0.00 0.00 0.00 -137.87 3 1 3 574.00 13.69 0.00 0.00 0.00 137.87 4 -574.00 -13.69 0.00 0.00 0.00 67.44 ************** END OF LATEST ANALYSIS RESULT ************** 24. UNIT INCH 25. START CONC DESIGN 26. CODE ACI 1999 27. TRACK 1.0 MEMB 2 28. FYMAIN 60.0 ALL 29. FC 4.0 ALL 30. CLB 1.4375 ALL 31. DESIGN BEAM 2 VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 4 =====================================================================

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BEAM NO. 2 DESIGN RESULTS - FLEXURE PER CODE ACI 318-99 20.00FT. FY - 60000. FC - 4000. SIZE - 10.00 X 16.00 INCHES HEIGHT BAR INFO FROM TO ANCHOR FT. IN. FT. IN. FT. IN. STA END _____________________________________________________________________ 1 0 + 2-5/8 2-NUM.10 0 + 0-0/0 20 + 0-0/0 YES YES |----------------------------------------------------------------| | CRITICAL POS MOMENT= 125.53 KIP-FT AT 10.00 FT, LOAD 1| | REQD STEEL= 2.48 IN2, RHO=0.0185, RHOMX=0.0214 RHOMN=0.0033 | | MAX/MIN/ACTUAL BAR SPACING= 10.16/ 2.54/ 4.73 INCH | | REQD. DEVELOPMENT LENGTH = 48.52 INCH | |----------------------------------------------------------------| Cracked Moment of Inertia Iz at above location = 1837.17 inch^4 *** A SUITABLE BAR ARRANGEMENT COULD NOT BE DETERMINED. REQD. STEEL = 2.792 IN2, MAX. STEEL PERMISSIBLE = 2.873 IN2 MAX NEG MOMENT = 137.87 KIP-FT, LOADING 1 *** A SUITABLE BAR ARRANGEMENT COULD NOT BE DETERMINED. REQD. STEEL = 2.792 IN2, MAX. STEEL PERMISSIBLE = 2.873 IN2 MAX NEG MOMENT = 137.87 KIP-FT, LOADING 1 ___ 2J____________________ 240.X 10.X 16_____________________ 3J____ | | | | | | | | | 2#10H 3. 0.TO 240. | ||=========================================================================|| | | |___________________________________________________________________________| _________ _________ _________ _________ _________ _________ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 2#10 | | 2#10 | | 2#10 | | 2#10 | | 2#10 | | 2#10 | | OO | | OO | | OO | | OO | | OO | | OO | | | | | | | | | | | | | |_________| |_________| |_________| |_________| |_________| |_________| ********************END OF BEAM DESIGN************************** 32. DESIGN COLUMN 1 VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 5 ==================================================================== COLUMN NO. 1 DESIGN PER ACI 318-99 - AXIAL + BENDING FY - 60000 FC - 4000 PSI, RECT SIZE - 14.00 X 16.00 INCHES, TIED AREA OF STEEL REQUIRED = 9.164 SQ. IN. BAR CONFIGURATION REINF PCT. LOAD LOCATION PHI ---------------------------------------------------------12 - NUMBER 8 4.232 1 END 0.700 (PROVIDE EQUAL NUMBER OF BARS ON EACH FACE) TIE BAR NUMBER 4 SPACING 14.00 IN ********************END OF COLUMN DESIGN RESULTS******************** 33. END CONC DESIGN 34. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:33 **** VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 6 ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * LEN LEVEL

84 — STAAD.Pro


* JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 7 Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb

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-----------------------------------------------------------------------------------------

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Compare theoretical answers to the STAAD solution.

Timoshenko, S., “Vibration Problems in Engineering”, Third Edition, D. Van Nostrand Company, Inc., 1955, page 322

The first five natural frequencies and the associated mode shapes are computed for the flexural motion of a simply supported beam. Figure 15-1: Simple beam diagram

Figure 15-2: Finite element model

The simply supported beam is divided into twenty spanwise beam elements. At nodes 1 and 21, all degrees of freedom except the rotation about the Z axis are restrained. For the remaining nodes, only the translation along Y and the rotation about Z are permitted. Both shear deformation and rotary inertia have been excluded from the model. The mass matrix is a diagonal matrix.

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Rectangular Section: 1 inch Width x 2 inch Depth Area = 2 in 2 J = b 3a/16 {16/3 - 3.36(b/a)[1 - 1/12(b/a) 4]} where a= 2 b= 1 J = 0.4578 inch 4 I = 1x23/12 inch4 2

I = 2x13/12 inch4 3

The natural bending frequencies, for a uniform beam with hinged ends, are given by: f = πn2/212(EIg/Aγ) 1/2 n

where f = natural frequency for mode n, in cycles per second n

l = span of the beam E = elastic modulus I = cross-section moment of inertia g = gravitational constant A = cross-section area γ = weight density The parameters used in the frequency equation are: l = 20 inches E = 10x106 psi I = 0.6667 inches4 g = 386.4 inches per second 2 A = 2.0 sq. inches γ = 0.1 pounds per cubic inch from which: f = n2x 445.685674 n

The table below shows the natural frequencies computed from the theoretical equation and the subspace iteration method available within STAAD. Frequencies are in cycles per second.

88 — STAAD.Pro


Table 15-1: Comparison of frequency values for verification problem no. 15 Mode Number

Theoretical

STAAD Basic Solver


1

445.686

445.506

445.506

2

1,782.74

1,782.01

1,782.01

3

4,011.17

4,009.41

4,009.41

4

7,130.97

7,127.25

7,127.25

5

11,142.1

11,134.25

11,134.25

STAAD PLANE STAAD VER. PROB. 15 UNIT POUND INCH JOINT COORD 1 0 0 0 21 20 0 0 MEMB INCI 1 1 2 20 MEMB PROP 1 TO 20 PRIS AX 2 IZ 0.6667 CONST E 10E6 ALL POISSON 0.3 ALL DENS 0.1 ALL CUT OFF MODE SHAPE 5 SUPP 1 21 FIXED BUT MZ 2 TO 20 FIXED BUT FY MZ LOAD 1 SELF X 1.0 SELF Y 1.0 MODAL CALC REQ PERF ANALY FINISH

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90 — STAAD.Pro


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:38 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE STAAD VER. PROB. 15 INPUT FILE: ver15.STD 2. * NATURAL MODES OF A SIMPLE BEAM 4. UNIT POUND INCH 5. JOINT COORD 6. 1 0 0 0 21 20 0 0 7. MEMB INCI 8. 1 1 2 20 9. MEMB PROP 10. 1 TO 20 PRIS AX 2 IZ 0.6667 11. CONST 12. E 10E6 ALL 13. POISSON 0.3 ALL 14. DENS 0.1 ALL 15. CUT OFF MODE SHAPE 5 16. SUPP 17. 1 21 FIXED BUT MZ 18. 2 TO 20 FIXED BUT FY MZ 19. LOAD 1 20. SELF X 1.0 21. SELF Y 1.0 22. MODAL CALC REQ 23. PERF ANALY P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 21/ 20/ 21 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 4 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 40 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB STAAD VER. PROB. 15 -- PAGE NO. 2 * NATURAL MODES OF A SIMPLE BEAM NUMBER OF MODES REQUESTED = 5 NUMBER OF EXISTING MASSES IN THE MODEL = 19 NUMBER OF MODES THAT WILL BE USED = 5 STAAD VER. PROB. 15 -- PAGE NO. 3 * NATURAL MODES OF A SIMPLE BEAM CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 445.506 0.00224 9.509E-16 2 1782.012 0.00056 1.934E-13 3 4009.410 0.00025 4.051E-11 4 7127.250 0.00014 1.334E-09 5 11134.253 0.00009 1.251E-08 STAAD VER. PROB. 15 -- PAGE NO. 4 * NATURAL MODES OF A SIMPLE BEAM The following Frequencies are estimates that were calculated. These are for information only and will not be used. Remaining values are either above the cut off mode/freq values or are of low accuracy. To use these frequencies, rerun with a higher cutoff mode (or mode + freq) value. CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 6 16027.429 0.00006 2.582E-08 7 21800.588 0.00005 5.322E-08

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8 9

28441.877 0.00004 4.956E-06 35929.844 0.00003 6.604E-05 MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED MODE X Y Z WEIGHT 1 0.000000E+00 3.228953E+00 0.000000E+00 2.000000E+00 2 0.000000E+00 3.801267E-26 0.000000E+00 2.000000E+00 3 0.000000E+00 3.469944E-01 0.000000E+00 2.000000E+00 4 0.000000E+00 3.572514E-19 0.000000E+00 2.211146E+00 5 0.000000E+00 1.165685E-01 0.000000E+00 2.000000E+00 MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 0.00 84.97 0.00 0.000 84.972 0.000 2 0.00 0.00 0.00 0.000 84.972 0.000 3 0.00 9.13 0.00 0.000 94.104 0.000 4 0.00 0.00 0.00 0.000 94.104 0.000 5 0.00 3.07 0.00 0.000 97.171 0.000 24. FINISH STAAD VER. PROB. 15 -- PAGE NO. 5 * NATURAL MODES OF A SIMPLE BEAM *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:38 **** ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ STAAD VER. PROB. 15 -- PAGE NO. 6 * NATURAL MODES OF A SIMPLE BEAM Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb

92 — STAAD.Pro


01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

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94 — STAAD.Pro



Blevins, Robert D., “Formulas for Natural Frequency and Mode Shape,” Van Nostrand Reinhold Company, 1979, Page 240.

A flat circular plate is simply supported around the entire perimeter. The first six modes and their associated natural frequencies are to be computed using the subspace iteration method offered by STAAD. This problem demonstrates that the natural frequencies of an axi-symmetric structure can be accurately computed utilizing a 180 degree model with the appropriate boundary conditions. Figure 16-1: Diagram of circular plate

The 180 degree sector was modeled using radial lines at intervals of 15 degrees. Tangential lines were then located utilizing a relationship such that the aspect ratio of the quad-plate elements was approximately 1.0. All rotations normal to the plane of the plate were restrained. In-plane translations for all nodes were restrained because the theoretical solution does not consider inplane effects. Rotations about the global Y axis for the nodes at X=0.0 were restrained because this is a symmetry boundary. Z translation of all nodes on the outside radius were restrained to provide for the simply-supported condition.

95 — STAAD.Pro


Figure 16-2: Finite model for half circular plate

It should be noted that the outside edge of the plate is a series of secant lines instead of a true arc. This will result in a loss of about 1% of the plate’s true mass or about .5% of the mass that is effective for this problem. Therefore, it is not unlikely that a few natural frequencies will be lower than the theoretical values instead of higher which is typical for a finite element analysis using plate elements. In addition, a true simple-support condition for this problem would require restraining the component of rotation that is radial to the outside edge.

From the reference case 2 in Table 11-1, the first six natural frequencies of the plate are described by the following equation:

f ij

=

l ij2 2p a

Eh3 2

(

12g 1 -

n 2)

= dimensionless parameter associated with the mode indices i,j i = number of nodal diameters in this mode shape j = number of nodal circles in this mode shape not counting the boundary ν = Poisson’s ratio E = Elastic Modulus h = plate thickness γ = mass of plate per unit area a = radius of plate The numerical values used for this example are:

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ν = 0.30 E = 10.0x10P 6P psi h = 0.10 inches γ = (0.10 lb /in3)(0.10 in)/(386.4 lb -in/lb -s2) = 2.588(10)-5 lb -s2/in3 m

m

f

f

a = 10.0 inches with the numerical values used above 1

Eh

2p a

2

12g(1 -

3 n

2

)

=

(10.0 ⋅ 10 6)(0.10)3

1 2

-5

2p (10.0)

2

12(2.588 ⋅ 10 )[1 - (0.3) ]

= 9.467

cycles/sec.

cycles/sec λ 2 is tabulated from the reference as follows: ij

Table 16-1: Values of λ 2

ij

Mode Number

ij

Number of Nodal Circles (j)

1

4.977

0

0

2

13.94

1

0

3

25.65

2

0

4

29.76

0

1

3

0

1

1

5(l) 6 (l)

Number of Nodal Diameters (i)

λ2

48.51

not tabulated in the reference

Table 16-2: Comparison of frequency values, Hz, for verification problem no. 16 Mode Number

STAAD Basic STAAD Advanced Solver Solver

1

47.12

46.21

46.21

2

132.0

130.54

130.54

3

242.8

240.15

240.15

4

281.7

283.03

283.03

373.2

373.2

466.58

466.58

5* 6

97 — STAAD.Pro

Theoretical

459.3


*The reference did not tabulate a value of for the fifth mode of the structure, hence a comparison with the theoretical value of this mode cannot be made.

All anti-symmetric mode shapes for the 360 degree circular plate were captured by the 180 degree model with a phase angle included in the calculation. Some of the difference between the theoretical and STAAD frequencies is attributed to the loss of mass due to the piecewise secant representation of the outer radius and, since this mass is about 1 percent lower than for a true circular plate, it is not surprising that the first few modes are lower than the theoretical solution.

STAAD SPACE STAAD VER. PROB. 16 * NATURAL FREQUENCIES OF A CIRCULAR PLATE UNIT POUND INCH JOINT COORD CYLINDRICAL 1 1 -90 0 13 1 90 0 REP 2 1.244 0 0 REP 1 1.051 0 0 REP 1 1.367 0 0 REP 1 1.779 0 0 REP 1 2.315 0 0 JOINT COORD 1000 0 0 0 ELEM INCI 1 1000 1 2 ; 2 1000 2 3 ; 3 1000 3 4 ; 4 1000 4 5 ; 5 1000 5 6 6 1000 6 7 ; 7 1000 7 8 ; 8 1000 8 9 ; 9 1000 9 10 ; 10 1000 10 11 11 1000 11 12 ; 12 1000 12 13 13 1 14 15 2 TO 24 REP 5 12 13 ELEM PROP 1 TO 84 TH 0.1 CONST E 10.0E6 ALL POISS 0.3 ALL DENS 0.1 ALL SUPP * CENTRE OF CIRCLE

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1000 FIXED BUT FZ MX * INTERIOR NODES 2 TO 12 15 TO 25 28 TO 38 41 TO 51 54 TO 64 67 TO 77 FIXED BUT FZ MX MY * NODES ALONG CIRCUMFERENCE 79 TO 91 FIXED BUT MX MY * NODES ALONG DIAMETER EXCEPT THE TWO AT THE ENDS OF THE DIAMETER. 1 TO 66 BY 13 13 TO 78 BY 13 FIXED BUT FZ MX LOAD 1 SELF X 1.0 SELF Y 1.0 SELF Z 1.0 MODAL CALC REQ PERF ANALY FINI

99 — STAAD.Pro


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:45 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE STAAD VER. PROB. 16 INPUT FILE: ver16.STD 2. * NATURAL FREQUENCIES OF A CIRCULAR PLATE 4. UNIT POUND INCH 5. JOINT COORD CYLINDRICAL 6. 1 1 -90 0 13 1 90 0 7. REP 2 1.244 0 0 8. REP 1 1.051 0 0 9. REP 1 1.367 0 0 10. REP 1 1.779 0 0 11. REP 1 2.315 0 0 13. JOINT COORD 14. 1000 0 0 0 16. ELEM INCI 17. 1 1000 1 2 ; 2 1000 2 3 ; 3 1000 3 4 ; 4 1000 4 5 ; 5 1000 5 6 18. 6 1000 6 7 ; 7 1000 7 8 ; 8 1000 8 9 ; 9 1000 9 10 ; 10 1000 10 11 19. 11 1000 11 12 ; 12 1000 12 13 21. 13 1 14 15 2 TO 24 22. REP 5 12 13 24. ELEM PROP 25. 1 TO 84 TH 0.1 27. CONST 28. E 10.0E6 ALL 29. POISS 0.3 ALL 30. DENS 0.1 ALL 32. SUPP 34. * CENTRE OF CIRCLE 35. 1000 FIXED BUT FZ MX 37. * INTERIOR NODES 38. 2 TO 12 15 TO 25 28 TO 38 41 TO 51 54 TO 64 39. 67 TO 77 FIXED BUT FZ MX MY 41. * NODES ALONG CIRCUMFERENCE 42. 79 TO 91 FIXED BUT MX MY 44. * NODES ALONG DIAMETER EXCEPT THE TWO AT THE ENDS OF THE DIAMETER. 45. 1 TO 66 BY 13 13 TO 78 BY 13 FIXED BUT FZ MX 47. LOAD 1 48. SELF X 1.0 49. SELF Y 1.0 50. SELF Z 1.0 51. MODAL CALC REQ 52. PERF ANALY STAAD VER. PROB. 16 -- PAGE NO. * NATURAL FREQUENCIES OF A CIRCULAR PLATE P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 92/ 84/ 92 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 91/ 13/ 40 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 250 SIZE OF STIFFNESS MATRIX = 10 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.8/ 120711.0 MB NUMBER OF MODES REQUESTED = 6 NUMBER OF EXISTING MASSES IN THE MODEL = 79 NUMBER OF MODES THAT WILL BE USED = 6 STAAD VER. PROB. 16 -- PAGE NO.

2

3

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* NATURAL FREQUENCIES OF A CIRCULAR PLATE CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 46.211 0.02164 5.178E-16 2 130.541 0.00766 1.038E-15 3 240.146 0.00416 2.045E-16 4 283.028 0.00353 8.835E-16 5 373.198 0.00268 5.081E-16 6 466.579 0.00214 2.601E-08 STAAD VER. PROB. 16 -- PAGE NO. 4 * NATURAL FREQUENCIES OF A CIRCULAR PLATE The following Frequencies are estimates that were calculated. These are for information only and will not be used. Remaining values are either above the cut off mode/freq values or are of low accuracy. To use these frequencies, rerun with a higher cutoff mode (or mode + freq) value. CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 7 527.844 0.00189 6.230E-13 8 672.921 0.00149 2.235E-07 9 701.137 0.00143 6.994E-10 10 712.175 0.00140 5.522E-07 11 888.597 0.00113 1.377E-08 12 903.499 0.00111 5.277E-07 MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED MODE X Y Z WEIGHT 1 0.000000E+00 0.000000E+00 1.053697E+00 4.537235E-01 2 0.000000E+00 0.000000E+00 2.213951E-10 3.944625E-01 3 0.000000E+00 0.000000E+00 1.886318E-07 3.935445E-01 4 0.000000E+00 0.000000E+00 1.275807E-01 1.752588E-01 5 0.000000E+00 0.000000E+00 1.060158E-08 4.222042E-01 6 0.000000E+00 0.000000E+00 7.873980E-10 2.165125E-01 MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 0.00 0.00 86.78 0.000 0.000 86.780 2 0.00 0.00 0.00 0.000 0.000 86.780 3 0.00 0.00 0.00 0.000 0.000 86.780 4 0.00 0.00 10.51 0.000 0.000 97.287 5 0.00 0.00 0.00 0.000 0.000 97.287 6 0.00 0.00 0.00 0.000 0.000 97.287 STAAD VER. PROB. 16 -- PAGE NO. 5 * NATURAL FREQUENCIES OF A CIRCULAR PLATE 53. FINI STAAD VER. PROB. 16 -- PAGE NO. 6 * NATURAL FREQUENCIES OF A CIRCULAR PLATE *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:46 **** ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ STAAD VER. PROB. 16 -- PAGE NO. 7

101 — STAAD.Pro


* NATURAL FREQUENCIES OF A CIRCULAR PLATE Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

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Blevins, Robert D., ”Formulas for Natural Frequency and Mode Shape,” Van Nostrand Reinhold Company, 1979, page 258.

A flat rectangular plate is simply supported on all four sides. The first six modes and their associated natural frequencies are to be computed for this structure using the subspace iteration method offered by STAAD. This problem also demonstrates that the mesh refinement can be chosen to accurately calculate modes of interest based on the expected mode shapes. Figure 17-1: Simply supported, rectangular plate

L = 45 in., W = 30 in., t = 0.2 in.

A plate with an aspect ratio of 1.5 was used so that comparison could be made with theoretical results tabulated for plates in the reference. An equally spaced mesh was utilized in both the x and the y dimensions of the plate. The number of elements in each dimension was determined on the basis of the highest mode of interest. Since the number of half-waves in the sixth mode is 3 in the length dimension and 2 in the width dimension, a node spacing of 3.75 inches results in each half- wave being represented by four elements which means that no element will be expected to

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deform in double curvature. The simply supported edge condition requires that translation normal to the plane of the plate be restrained for these edge nodes. Rotations normal to the plate were restrained for all nodes. Figure 17-2: Model: finite element meshed

From the reference case 16 in Table 11-4, the first six natural frequencies of the plate are described by the following equations: f ij

=

l ij2 2p a

Eh3 2

(

12g 1 -

n 2)

= dimensionless parameter associated with the mode indices i, j i = number of half-waves in this mode shape along the horizontal axis j = number of half-waves in this mode shape along the vertical axis ν = Poisson’s ratio E = elastic modulus h = plate thickness γ = mass of material per unit area a = length of plate b = width of plate

104 — STAAD.Pro


The numerical values used for this example are: ν = 0.30 E =30.0x106 psi h=0.2 inches γ = (0.282 lb /in3)(0.20 in)/(386.4 lb -in/lb -s2) = .1460(10)-4 lb -s2/in3 m

m

f

f

a = 45.0 inches b = 30.0 inches with the numerical values used above 1

Eh

2p a 2

12g(1 -

1

(30.0 ⋅ 106)(0.20)3

2p (10.0)2

12(1.460 ⋅ 10- 4)[1 - (0.3)2 ]

3 n

2

)

=

= 0.9644

cycles/sec.

λ 2 is tabulated from the reference as follows: ij

Table 17-1: Values of λ 2

ij

Mode Number

λ2

ij

Number of Half-Waves in Length (i)

Number of Half-Waves in Width (j)

1

32.08

1

1

2

61.69

2

1

3

98.70 1

2

4

111.0

3

1

5

128.3

2

2

6

177.7

3

2

Table 17-2: Comparison of frequency values, Hz, for verificatoin problem no. 17 Mode Number

Theoretical

STAAD Basic Solver


1

30.94

30.6

30.6

2

59.49

58.72

58.72

3

95.18

95.06

95.06

4

107.1

106.28

106.28

5

123.7

122.09

122.09

6

171.3

168.0

168.0

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As was noted earlier, the node spacing was based on the highest mode of interest. It follows that the difference between the theoretical and STAAD frequencies generally increases with increasing mode sequence.

STAAD SPACE STAAD VER. PROB. 17. * NATURAL FREQUENCIES OF A RECTANGULAR PLATE UNIT POUND INCH JOINT COORD 1 0 0 0 13 45 0 0 REP ALL 8 0 3.75 0 ELEM INCI 1 1 2 15 14 TO 12 REP 7 12 13 ELEM PROP 1 TO 96 TH 0.2 CONST E 30.0E6 ALL DENS 0.282 ALL POISSON 0.3 ALL CUT OFF MODE SHAPE 6 CUT OFF FREQ 1000 SUPPORT * CORNER NODES 1 13 105 117 FIXED BUT MX MY * NODES ALONG Y=0 AND Y=30 2 TO 12 106 TO 116 FIXED BUT MX MY * NODES ALONG X=0 14 TO 92 BY 13 FIXED BUT MX MY * NODES ALONG X=45 26 TO 104 BY 13 FIXED BUT MX MY * INTERIOR NODES 15 TO 25 28 TO 38 41 TO 51 54 TO 64 67 TO 77 80 TO 90 93 TO 103 FIXED BUT FZ MX MY

106 — STAAD.Pro


LOAD 1 SELF X 1 SELF Y 1 SELF Z 1 MODAL CALC REQ PERF ANALY FINI

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107


**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:51 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE STAAD VER. PROB. 17 INPUT FILE: ver17.STD 2. * NATURAL FREQUENCIES OF A RECTANGULAR PLATE 4. UNIT POUND INCH 5. JOINT COORD 6. 1 0 0 0 13 45 0 0 7. REP ALL 8 0 3.75 0 8. ELEM INCI 9. 1 1 2 15 14 TO 12 10. REP 7 12 13 11. ELEM PROP 12. 1 TO 96 TH 0.2 13. CONST 14. E 30.0E6 ALL 15. DENS 0.282 ALL 16. POISSON 0.3 ALL 17. CUT OFF MODE SHAPE 6 18. CUT OFF FREQ 1000 19. SUPP 21. * CORNER NODES 22. 1 13 105 117 FIXED BUT MX MY 24. * NODES ALONG Y=0 AND Y=30 25. 2 TO 12 106 TO 116 FIXED BUT MX MY 27. * NODES ALONG X=0 28. 14 TO 92 BY 13 FIXED BUT MX MY 30. * NODES ALONG X=45 31. 26 TO 104 BY 13 FIXED BUT MX MY 33. * INTERIOR NODES 34. 15 TO 25 28 TO 38 41 TO 51 54 TO 64 67 TO 77 80 TO 90 35. 93 TO 103 FIXED BUT FZ MX MY 37. LOAD 1 38. SELF X 1 39. SELF Y 1 40. SELF Z 1 41. MODAL CALC REQ 42. PERF ANALY STAAD VER. PROB. 17 -- PAGE NO. 2 * NATURAL FREQUENCIES OF A RECTANGULAR PLATE P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 117/ 96/ 117 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 14/ 14/ 43 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 311 SIZE OF STIFFNESS MATRIX = 14 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.9/ 120710.9 MB NUMBER OF MODES REQUESTED = 6 NUMBER OF EXISTING MASSES IN THE MODEL = 77 NUMBER OF MODES THAT WILL BE USED = 6 STAAD VER. PROB. 17 -- PAGE NO. 3 * NATURAL FREQUENCIES OF A RECTANGULAR PLATE CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 30.599 0.03268 1.968E-16 2 58.724 0.01703 4.325E-13

108 — STAAD.Pro


3 95.063 0.01052 9.652E-11 4 106.277 0.00941 8.480E-10 5 122.092 0.00819 1.381E-08 6 168.009 0.00595 9.194E-07 STAAD VER. PROB. 17 -- PAGE NO. 4 * NATURAL FREQUENCIES OF A RECTANGULAR PLATE The following Frequencies are estimates that were calculated. These are for information only and will not be used. Remaining values are either above the cut off mode/freq values or are of low accuracy. To use these frequencies, rerun with a higher cutoff mode (or mode + freq) value. CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 7 173.592 0.00576 3.784E-07 8 204.044 0.00490 1.762E-06 9 229.811 0.00435 4.807E-05 10 233.369 0.00429 2.127E-05 11 261.140 0.00383 4.621E-05 MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED MODE X Y Z WEIGHT 1 0.000000E+00 0.000000E+00 4.833474E+01 1.915442E+01 2 0.000000E+00 0.000000E+00 4.228619E-20 1.920213E+01 3 0.000000E+00 0.000000E+00 1.629244E-18 1.925533E+01 4 0.000000E+00 0.000000E+00 4.837136E+00 1.927464E+01 5 0.000000E+00 0.000000E+00 1.069665E-13 1.927599E+01 6 0.000000E+00 0.000000E+00 7.199120E-11 1.936302E+01 MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 0.00 0.00 79.15 0.000 0.000 79.146 2 0.00 0.00 0.00 0.000 0.000 79.146 3 0.00 0.00 0.00 0.000 0.000 79.146 4 0.00 0.00 7.92 0.000 0.000 87.066 5 0.00 0.00 0.00 0.000 0.000 87.066 6 0.00 0.00 0.00 0.000 0.000 87.066 43. FINI STAAD VER. PROB. 17 -- PAGE NO. 5 * NATURAL FREQUENCIES OF A RECTANGULAR PLATE STAAD VER. PROB. 17 -- PAGE NO. 6 * NATURAL FREQUENCIES OF A RECTANGULAR PLATE *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:52 **** ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ STAAD VER. PROB. 17 -- PAGE NO. 7 * NATURAL FREQUENCIES OF A RECTANGULAR PLATE Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe

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09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

110 — STAAD.Pro

Compare the results from STAAD's subspace iteration method with the results from EASE2® and ANSYS®.

1. Problem 1, from the ASME 1972 Program Verification and Qualification Library 2. DeSalvo, G.J., and Swanson, J.A., “ANSYS Engineering Analysis System Examples Manual”, Swanson Analysis Systems, Inc., 1979, Example Problem No. 2. 3. Peterson, F.E., “EASE2 Elastic Analysis for Structural Engineering Example Problem Manual”, Engineering Analysis Corporation, 1981, Example 2.03.

A three dimensional frame is analyzed for its natural frequencies and the associated mode shapes using the subspace iteration method offered by STAAD. Figure 18-1: Frame model

All dimensions are in inches.

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The only entity present in the model is the general purpose three dimensional beam.

All the beam elements have the same cross section: Outside radius, Ro = 1.1875 in. Inside radius, Ri = 1.0335 in. Area = π(Ro2 - Ri2) = 1.074532 in 2 Moment of Inertia, I = π/4(Ro4 - Ri4) I = 0.665747 in4 Torsion constant = twice the inertia, for closed circular sections = 1.331494 in 4 The expression for the shear flexibility factor is derived from the ratio of maximum shear stress to the average shear stress: α = AQ/Ib Where the four items – A, Q, I, and b are properties of the half cross-section about the centerline. For the circular section they are: A = π/2(Ro2 - Ri2) Q = 2/3(Ro3 - Ri3) I = π/8(Ro4 - Ri4) I = 2(Ro - Ri) The final expression for the shear flexibility factor, for a circular tube section is: a

=

AQ Ib

3

=

Ro

4 3

-

R

3

i

(R o - R i )(R o - R i) 2

2

α = 1.993620 Hence the shear area is entered as AY = Cross Section Area / α = 1.074532 / 1.99362 = 0.538985 in 2

The following table compares Twenty-Four Natural Frequencies Table 18-1: Comparison of natural frequency values (cycles per second) for verification problem no. 18 Mode Number

1

112 — STAAD.Pro

DeSalvo and Swanson2

111.52

Peterson STAAD Basic 3 Solver


111.53

111.23

111.23


STAAD SPACE STAAD VER. PROB. 18 * NATURAL FREQUENCIES OF A SPACE FRAME UNIT POUND INCH JOINT COORD 1 0 0 0 ; 2 27.25 0 0 3 0 10 0 ; 4 27.25 10 0 5 0 18.625 0 ; 6 8.625 18.625 0 ; 7 18.625 18.625 0 ; 8 27.25 18.625 0

9 0 18.625 8.625 ; 10 27.25 18.625 8.625

11 0 0 17.25 ; 12 27.25 0 17.25 13 0 10 17.25 ; 14 27.25 10 17.25 15 0 18.625 17.25 ; 16 8.625 18.625 17.25 17 18.625 18.625 17.25 ; 18 27.25 18.625 17.25

MEMB INCI 1 1 3 ; 2 2 4 ; 3 3 5 ; 4 4 8 5 5 6 7

8 5 9 ; 9 8 10 ; 10 9 15 ; 11 10 18

12 11 13 ; 13 12 14 ; 14 13 15 ; 15 14 18 16 15 16 ; 17 16 17 ; 18 17 18

MEMB PROP 1 TO 18 PRIS AX 1.074532 IZ 0.665747 IY 0.665747 IX 1.331494 AY 0.538985 AZ 0.538985 * AY 1.88 AZ 1.88

CONST E 27.9E6 ALL POISS 0.3 ALL CUT OFF MODE SHAPE 24

114 — STAAD.Pro


1 2 11 12 FIXED

LOAD 1 JOINT LOAD 3 4 13 14 FX 3.4517 FY 3.4517 FZ 3.4517 6 7 16 17 FX 3.4517 FY 3.4517 FZ 3.4517 9 10 FX 3.4517 FY 3.4517 FZ 3.4517 5 8 15 18 FX 9.7973 FY 9.7973 FZ 9.7973

MODAL CALC REQ PERF ANALY FINI

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**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 5:56 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE STAAD VER. PROB. 18 INPUT FILE: ver18.STD 2. * NATURAL MODES OF A SPACE FRAME 4. UNIT POUND INCH 5. JOINT COORD 6. 1 0 0 0 ; 2 27.25 0 0 7. 3 0 10 0 ; 4 27.25 10 0 8. 5 0 18.625 0 ; 6 8.625 18.625 0 ; 7 18.625 18.625 0 ; 8 27.25 18.625 0 10. 9 0 18.625 8.625 ; 10 27.25 18.625 8.625 12. 11 0 0 17.25 ; 12 27.25 0 17.25 13. 13 0 10 17.25 ; 14 27.25 10 17.25 14. 15 0 18.625 17.25 ; 16 8.625 18.625 17.25 15. 17 18.625 18.625 17.25 ; 18 27.25 18.625 17.25 17. MEMB INCI 18. 1 1 3 ; 2 2 4 ; 3 3 5 ; 4 4 8 19. 5 5 6 7 21. 8 5 9 ; 9 8 10 ; 10 9 15 ; 11 10 18 23. 12 11 13 ; 13 12 14 ; 14 13 15 ; 15 14 18 24. 16 15 16 ; 17 16 17 ; 18 17 18 26. MEMB PROP 27. 1 TO 18 PRIS AX 1.074532 IZ 0.665747 IY 0.665747 IX 1.331494 28. AY 0.538985 AZ 0.538985 29. * AY 1.88 AZ 1.88 31. CONST 32. E 27.9E6 ALL 33. POISS 0.3 ALL 34. CUT OFF MODE SHAPE 24 36. SUPP 37. 1 2 11 12 FIXED 39. LOAD 1 40. JOINT LOAD 41. 3 4 13 14 FX 3.4517 FY 3.4517 FZ 3.4517 42. 6 7 16 17 FX 3.4517 FY 3.4517 FZ 3.4517 43. 9 10 FX 3.4517 FY 3.4517 FZ 3.4517 44. 5 8 15 18 FX 9.7973 FY 9.7973 FZ 9.7973 46. MODAL CALC REQ 47. PERF ANALY STAAD VER. PROB. 18 -- PAGE NO. 2 * NATURAL MODES OF A SPACE FRAME P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 18/ 18/ 4 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 8/ 4/ 30 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 84 SIZE OF STIFFNESS MATRIX = 3 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.1/ 120710.9 MB NUMBER OF MODES REQUESTED = 24 NUMBER OF EXISTING MASSES IN THE MODEL = 42 NUMBER OF MODES THAT WILL BE USED = 24 STAAD VER. PROB. 18 -- PAGE NO. 3 * NATURAL MODES OF A SPACE FRAME CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 111.236 0.00899 7.150E-16

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2 115.801 0.00864 4.398E-16 3 137.169 0.00729 3.134E-16 4 215.799 0.00463 1.266E-15 5 404.271 0.00247 4.330E-16 6 422.642 0.00237 5.283E-16 7 451.600 0.00221 0.000E+00 8 549.012 0.00182 1.565E-16 9 733.589 0.00136 0.000E+00 10 758.563 0.00132 3.280E-16 11 851.355 0.00117 3.906E-16 12 892.281 0.00112 3.556E-16 13 893.060 0.00112 0.000E+00 14 910.829 0.00110 5.881E-12 15 932.286 0.00107 2.171E-16 16 956.391 0.00105 2.063E-16 17 964.012 0.00104 7.216E-10 18 967.267 0.00103 0.000E+00 19 981.536 0.00102 0.000E+00 20 1009.256 0.00099 3.706E-16 21 1070.562 0.00093 1.419E-10 22 1123.161 0.00089 4.488E-16 23 1149.368 0.00087 9.081E-09 24 1199.882 0.00083 3.933E-16 STAAD VER. PROB. 18 -- PAGE NO. 4 * NATURAL MODES OF A SPACE FRAME The following Frequencies are estimates that were calculated. These are for information only and will not be used. Remaining values are either above the cut off mode/freq values or are of low accuracy. To use these frequencies, rerun with a higher cutoff mode (or mode + freq) value. CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 25 1262.045 0.00079 7.109E-16 26 1352.368 0.00074 0.000E+00 27 1355.475 0.00074 7.348E-10 28 1410.628 0.00071 1.897E-16 29 1512.064 0.00066 3.302E-16 30 1567.343 0.00064 3.073E-16 31 1926.045 0.00052 4.070E-16 32 1943.161 0.00051 1.999E-16 33 3654.783 0.00027 5.062E-08 34 3659.116 0.00027 4.511E-16 35 4514.280 0.00022 7.409E-16 36 4514.644 0.00022 7.422E-08 37 4515.631 0.00022 5.923E-16 38 4516.026 0.00022 1.481E-16 39 4815.936 0.00021 3.906E-16 40 5312.712 0.00019 4.279E-16 MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED MODE X Y Z WEIGHT 1 6.984127E+01 2.148148E-33 2.116575E-28 6.127270E+01 2 1.278059E-28 4.260871E-33 7.005318E+01 5.765801E+01 3 1.334786E-26 1.506346E-32 7.258520E-26 7.213568E+01 4 5.363809E-23 8.246502E-38 9.476748E-28 7.915617E+01 5 5.181462E-30 4.244586E-03 8.548127E-32 1.532638E+01 6 1.574093E-27 1.825469E+01 3.599063E-35 1.469096E+01 7 1.297531E-27 1.703203E-29 5.112395E-03 1.450510E+01 8 4.947173E-32 1.476836E-32 2.966451E-01 1.825927E+01 9 6.029626E-28 9.521517E+00 6.548318E-27 1.177227E+01 10 9.808873E-04 2.461898E-29 7.138047E-30 1.174657E+01 11 1.321193E+00 4.883939E-31 5.697600E-24 1.582130E+01 12 4.394276E-25 1.911258E+00 1.705243E-24 1.624941E+01 13 1.722238E+00 2.888943E-26 1.809548E-24 3.802992E+01 14 2.862893E-26 2.885970E-28 2.865256E-30 2.195000E+01 15 2.786326E-28 1.289225E-28 2.363041E-01 1.628835E+01 16 1.013788E-24 4.122944E+00 1.025583E-24 1.648078E+01 17 2.160889E-24 4.239236E-28 1.355195E-26 1.622822E+01

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18 3.256494E-26 1.184829E-28 3.083967E+00 1.640511E+01 19 3.491379E-01 1.623903E-30 1.402550E-24 2.835636E+01 20 3.469303E-25 1.122183E+01 5.217990E-24 2.560370E+01 21 9.923317E-24 1.878264E-27 1.264702E-26 3.464233E+01 STAAD VER. PROB. 18 -- PAGE NO. 5 * NATURAL MODES OF A SPACE FRAME 22 3.635978E-01 1.612759E-28 2.105646E-25 3.137066E+01 23 3.474316E-25 3.040856E-29 1.020214E-23 1.555328E+01 24 6.381997E-02 1.963886E-28 1.643944E-29 2.520960E+01 STAAD VER. PROB. 18 -- PAGE NO. 6 * NATURAL MODES OF A SPACE FRAME MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 94.76 0.00 0.00 94.756 0.000 0.000 2 0.00 0.00 95.04 94.756 0.000 95.044 3 0.00 0.00 0.00 94.756 0.000 95.044 4 0.00 0.00 0.00 94.756 0.000 95.044 5 0.00 0.01 0.00 94.756 0.006 95.044 6 0.00 24.77 0.00 94.756 24.773 95.044 7 0.00 0.00 0.01 94.756 24.773 95.051 8 0.00 0.00 0.40 94.756 24.773 95.453 9 0.00 12.92 0.00 94.756 37.691 95.453 10 0.00 0.00 0.00 94.758 37.691 95.453 11 1.79 0.00 0.00 96.550 37.691 95.453 12 0.00 2.59 0.00 96.550 40.284 95.453 13 2.34 0.00 0.00 98.887 40.284 95.453 14 0.00 0.00 0.00 98.887 40.284 95.453 15 0.00 0.00 0.32 98.887 40.284 95.774 16 0.00 5.59 0.00 98.887 45.878 95.774 17 0.00 0.00 0.00 98.887 45.878 95.774 18 0.00 0.00 4.18 98.887 45.878 99.958 19 0.47 0.00 0.00 99.360 45.878 99.958 20 0.00 15.23 0.00 99.360 61.103 99.958 21 0.00 0.00 0.00 99.360 61.103 99.958 22 0.49 0.00 0.00 99.854 61.103 99.958 23 0.00 0.00 0.00 99.854 61.103 99.958 24 0.09 0.00 0.00 99.940 61.103 99.958 48. FINI *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 5:56 **** STAAD VER. PROB. 18 -- PAGE NO. 7 * NATURAL MODES OF A SPACE FRAME ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ STAAD VER. PROB. 18 -- PAGE NO. 8 * NATURAL MODES OF A SPACE FRAME Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name -----------------------------------------------------------------------------------------

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03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll 02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

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1. Biggs, John M., “Introduction to Structural Dynamics,” McGraw Hill, 1964, pp. 256-263 2. Blevins, Robert D.,“ Formulas for Natural Frequency and Mode Shape,” Van NostrandReinhold, 1979.

The supports of a simply supported beam are subjected to an acceleration time history. The maximum bending moment in the beam is computed for the first mode of the structure. This problem demonstrates the capabilities of STAAD to calculate the correct modal response of a structure utilizing response spectrum data. Figure 19-1: Simple span beam

The STAAD model consists of 11 nodes and 10 elastic beam elements. Node 1 is completely restrained with the exception of having rotational freedom in the Z direction, the remaining nodes are restrained except for X and Y displacements and Z rotations. Node 11 is additionally restrained against displacements in the Y direction to provide for the simple support condition . Only the contribution of the first mode of the structure is considered.

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Figure 19-2: Finite element model

Material Properties L = 240.0 inches E = 30 x 10 6 lb/in 2 EI = 1.0 x 10 10 lb-in2 m = 0.2 lb-sec 2 / in i n2 h = 14.0 in. From Reference 2, Table 8-1, page 108, the fundamental frequency of the beam is: 2

fi =

li

2p

EI 2

m

=

9.869 2p (240) (240)2

1.0(10) 0.2

10

= 6.098hz

The modal participation factor for the fundamental mode is: 1

=

G

ò 0 mϕ(x ) d x 1 2 ò 0 mϕ (x ) d x

Where the first mode shape, shape, φ(x) = sin(πx/1 sin(π x/1)) =

G

1 px m ò sin d x 0 1 1 px 2 m ò sin d x 0 1

=4/p

The maximum relative modal displacement is given by: A

max

= Γu0

max

Where: u0

max

= y'' /ω2(DLF) so

ω - 2π*6.098Hz y'' = 1.0g so

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max


(DLF)

max

= 1.648 at 6.098 Hz

therefore: A

max

= 4(1.648)(386.4)/ 4(1.648)(386.4)/[π(2π) [π(2π)2(6.098)2] = 0.5523 in.

The bending moment M = -EIδ 2u/(δx2) Where u for the t he first mode = A sin(πx/l) δ2u/(δx2) = -π 2/l2 A·sin(πx/l) M = AEI·(π 2/l2)·sin(πx/l) M

max

= A

EI·(π2/l2)

max

at x = l/2 M

max

= 1(10)10·(0.5523)·π2/(2402) = 946.351(10)3 lb·in

at x=l/2

Table 19-1: Comparison of max. moment in beam 5 for verification problem no. 19 Solution

Bendin nding g Moment ment (kip (kip-i -inc nch) h)

Theory

STAAD Basic Solver


946.351

947.09

947.09

STAAD STAAD SPACE SPACE STAAD STAAD VER. VER. PROB. PROB. 19 * RESP RESPON ONSE SE OF A SIMP SIMPLY LY SUPP SUPPOR ORTE TED D BEAM BEAM TO A SHOC SHOCK K SPEC SPECTR TRUM UM UNIT UNIT POUND POUND INCH INCH JOINT COORD 1 0 0 0 11 240 0 0 MEMB MEMB INCI INCI 1 1 2 10 MEMB MEMB PROP PROP 1 TO 10 PRIS PRIS YD 14.0 14.0 ZD 1.45 1.4577 777 7 AX 20.4 20.408 082 2 IX 40.0 40.0 IY 3.61 3.6139 39 IZ 333. 333.33 333 3 CONST E 30.0 30.0E6 E6 ALL ALL POISS POISS 0.3 ALL DENS DENS 3.7867 3.78672 2 ALL CUT CUT OFF OFF MODE MODE SHAP SHAPE E 1

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SUPPORT 1 FIXE FIXED D BUT BUT MZ 2 TO 10 FIXE IXED BUT FX FY MZ 11 FIXE FIXED D BUT BUT FX MZ LOAD LOAD 1 SELF SELF X 1.0 1.0 SELF SELF Y 1.0 1.0 SPEC SPECTR TRUM UM SRSS SRSS Y 1.0 1.0 ACC ACC DAMP DAMP 0.00 0.001 1 SCAL SCALE E 386. 386.4 4 0.15 0.15 1.64 1.648 8 ; 0.17 0.17 1.64 1.648 8 PERF PERF ANALY ANALY PRIN PRINT T MEMB MEMB FORC FORCE E LIST LIST 5 FINI

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**************************************************** * * * STAAD.Pro V8i SELECTseries2 * * Version 20.07.07.32 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 9, 2011 * * Time= 11: 6: 1 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE STAAD VER. PROB. 19 INPUT FILE: ver19.STD 2. * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A SHOCK SPECTRUM 3. UNIT POUND INCH 4. JOINT COORD 5. 1 0 0 0 11 240 0 0 6. MEMB INCI 7. 1 1 2 10 8. MEMB PROP 9. 1 TO 10 PRIS YD 14.0 ZD 1.45777 AX 20.4082 IX 40.0 IY 3.6139 IZ 333.333 10. CONST 11. E 30.0E6 ALL 12. POISS 0.3 ALL 13. DENS 3.78672 ALL 14. CUT OFF MODE SHAPE 1 15. SUPPORT 16. 1 FIXED BUT MZ 17. 2 TO 10 FIXED BUT FX FY MZ 18. 11 FIXED BUT FX MZ 19. LOAD 1 20. SELF X 1.0 21. SELF Y 1.0 22. SPECTRUM SRSS Y 1.0 ACC DAMP 0.001 SCALE 386.4 23. 0.15 1.648 ; 0.17 1.648 24. PERF ANALY P R O B L E M S T A T I S T I C S ----------------------------------NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 11/ 10/ 11 STAAD VER. PROB. 19 -- PAGE NO. 2 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOF TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 30 SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS REQRD/AVAIL. DISK SPACE = 12.0/ 120710.9 MB NUMBER OF MODES REQUESTED = 1 NUMBER OF EXISTING MASSES IN THE MODEL = 19 NUMBER OF MODES THAT WILL BE USED = 1 STAAD VER. PROB. 19 -- PAGE NO. 3 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 6.069 0.16476 2.208E-07 STAAD VER. PROB. 19 -- PAGE NO. 4 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S The following Frequencies are estimates that were calculated. These are for information only and will not be used. Remaining values are either above the cut off mode/freq values or are of low accuracy. To use these frequencies, rerun with a higher cutoff mode (or mode + freq) value. CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 2 23.959 0.04174 8.561E-07 3 52.682 0.01898 1.066E-08 MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED MODE X Y Z WEIGHT

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1 3.605170E-18 1.478714E+04 0.000000E+00 9.273617E+03 RESPONSE LOAD CASE 1 SRSS MODAL COMBINATION METHOD USED. DYNAMIC WEIGHT X Y Z 1.761987E+04 1.669251E+04 0.000000E+00 POUN MISSING WEIGHT X Y Z -1.761987E+04 -1.905373E+03 0.000000E+00 POUN MODAL WEIGHT X Y Z 3.605170E-18 1.478714E+04 0.000000E+00 POUN MODE ACCELERATION-G DAMPING ----------------------1 1.64933 0.00100 MODAL BASE ACTIONS FORCES IN POUN LENGTH IN INCH ----------------------------------------------------------MOMENTS ARE ABOUT THE ORIGIN MODE PERIOD FX FY FZ MX MY MZ 1 0.165 0.00 24388.86 0.00 0.00 0.00 2926662.97 STAAD VER. PROB. 19 -- PAGE NO. 5 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S MASS PARTICIPATION FACTORS IN PERCENT BASE SHEAR IN POUN ------------------------------------------------------MODE X Y Z SUMM-X SUMM-Y SUMM-Z X Y Z 1 0.00 88.59 0.00 0.000 88.585 0.000 0.00 24388.86 0.00 --------------------------TOTAL SRSS SHEAR 0.00 24388.86 0.00 TOTAL 10PCT SHEAR 0.00 24388.86 0.00 TOTAL ABS SHEAR 0.00 24388.86 0.00 25. PRINT MEMB FORCE LIST 5 STAAD VER. PROB. 19 -- PAGE NO. 6 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------ALL UNITS ARE -- POUN INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 5 1 5 0.02 1931.41 0.00 0.00 0.00 900734.25 6 0.02 1931.41 0.00 0.00 0.00 947088.00 ************** END OF LATEST ANALYSIS RESULT ************** 26. FINI *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAR 9,2011 TIME= 11: 6: 2 **** STAAD VER. PROB. 19 -- PAGE NO. 7 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S ************************************************************ * For questions on STAAD.Pro, please contact * * Bentley Systems or Partner offices * * * * Telephone Web / Email * * USA +1 (714) 974-2500 * * UK +44 (0) 808 101 9246 * * SINGAPORE +65 6225-6158 * * FRANCE +33 (0) 1 55238400 * * GERMANY +49 0931 40468 * * INDIA +91 (033) 4006-2021 * * JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp * * CHINA +86 21 6288 4040 * * THAILAND +66 (0)2645-1018/19 [email protected]* * * * Worldwide http://selectservices.bentley.com/en-US/ * * * ************************************************************ STAAD VER. PROB. 19 -- PAGE NO. 8 * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S Information about the key files in the current distribution Modification Date CRC Size (Bytes) File Name ----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe 02/22/2011 0xc181 08667136 SProStaadStl.exe 09/19/2003 0x2fc0 00081970 CMesh.dll 02/17/2011 0xa7c1 04276294 dbsectioninterface.dll

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02/22/2011 0x12c0 00294912 EC3Annex.dll 02/22/2011 0x2900 00376832 EuroCode3.dll 12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll 01/24/2001 0x9b40 00073728 LoadGen.dll 11/19/2010 0xeb80 00011264 MathExtensions.dll 09/25/2003 0x6340 00704512 MeshEngine.dll 02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll 09/22/2003 0xce00 00069632 QuadPlateEngine.dll 12/02/2010 0x5040 00073728 SteelCollection.dll 02/22/2011 0xca81 00024064 SteelDesign.dll 10/08/2010 0xa940 00072192 SteelSections.dll 05/29/2008 0x77c1 00106572 SurfMeshEngine.dll 10/08/2010 0x4680 00010752 UnitConversions.dll 02/08/2011 0xfc00 00974848 AISCSections.mdb 06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb 06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb 01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb 01/05/2005 0xcac1 03651584 aitctimbersections.mdb 05/01/2008 0xb001 00552960 aluminumsections.mdb 01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb 10/02/2008 0x40 00520192 AustralianSections.mdb 06/11/2010 0xa101 00585728 BritishSections.mdb 09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb 06/28/2005 0x8201 00327680 butlercoldformedsections.mdb 02/25/2008 0x2e01 00329728 CanadianSections.mdb 09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb 05/31/2005 0x9e81 00450560 canadiantimbersections.mdb 02/10/2010 0x94c1 00483328 ChineseSections.mdb 01/05/2005 0xd6c0 00600064 dutchsections.mdb 10/07/2010 0xd2c0 03596290 EuropeanSections.mdb 01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb 01/05/2005 0xd301 00202752 frenchsections.mdb 01/05/2005 0x11c1 00233472 germansections.mdb 10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb 12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb 12/08/2009 0xec1 00942080 IndianSections.mdb 01/05/2005 0xd540 00180224 iscoldformedsections.mdb 02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb 03/23/2006 0xa080 00200704 japanesesections.mdb 02/04/2011 0x3300 00495616 JindalSections.mdb 11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb 08/24/2007 0x3ec0 00454656 Koreansections.mdb 04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb 02/07/2005 0x9a00 00243712 mexicansteeltables.mdb 04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb 11/20/2009 0xf700 00428034 RussianSections.mdb 05/12/2009 0xe001 00237570 SouthAfricanSections.mdb 01/06/2005 0x9341 00194560 spanishsections.mdb 11/20/2009 0x5100 00368640 STO_ASChMSections.mdb 04/19/2007 0x7480 00223232 uscoldformedsections.mdb 10/31/2007 0x3700 00133120 VenezuelanSections.mdb -----------------------------------------------------------------------------------------

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Timoshenko, S., and Woinowsky-Krieger, S., “Theory of Plates and Shells”, Second Edition, McGraw-Hill, 1959, pages 162 - 165.

A rectangular plate is simply supported on all four sides. The transverse and longitudinal bending moments as well as the deflections at several points on the plate are computed. Figure 20-1: Rectangular plate model

L = 12 in., W = 16 in.

The plate is modeled using 1 in. X 1 in. size elements. At the corner nodes, all the degrees of freedom are considered restrained. For the nodes along the four edges, rotation is permitted about that edge.

From the Reference, equation (j), the expression for deflection normal to the plate surface is:

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129

20 Thermal Loading on a Simply Supported Rectangular Plate

w=-

at (1 + n ) 4 p 3h

2

mpx

sin ¥ åm =1,3,5¼ m3

 1 -

cosh

mpy

cosha m

 

where α = mπb/(2a) From the Reference, equation (k), the expressions for bending moment per unit width are M x =

M y =

4Dat (1 - n 2) ph at(1 - n 2)D h

¥ åm =1,3,5¼

-

sin

4Dat (1 - n 2 ) ph

m x

cosh

m y

m ⋅ cosha m

¥ åm =1,3,5¼

sin

mpx

cosh

mpy

m ⋅ cosha m

Where: α = Coefficient of Thermal Expansion t = Difference between the temperatures of the upper and lower surfaces of the plate ν = Poisson’s ratio h = Plate thickness a = Dimension of the plate along the x1 axis b = Dimension of the plate along the x2 axis E = Elastic Modulus D = Eh 3/[12(1 - ν2) The numerical values used for this example are: α = 12.0E-06 / °F t = 450 °F ν = 0.3 h = 0.3 in. a = 12 in. b = 16 in. E= 10.0E6 psi

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STAAD-PRO-V8i

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